Estimating Source Strength Parameters at DNAPL Contaminated Field Sites Using Historical Transect and Pumping Data

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Estimating Source Strength Parameters at DNAPL Contaminated Field Sites Using Historical Transect and Pumping Data
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1 online resource (116 p.)
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english
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Donahue,Rachel E
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University of Florida
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Master's ( M.E.)
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University of Florida
Degree Disciplines:
Environmental Engineering Sciences
Committee Chair:
Annable, Michael D
Committee Members:
Hatfield, Kirk
Jawitz, James W

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dnapl -- equilibrium -- function -- model -- source -- streamtube -- strength
Environmental Engineering Sciences -- Dissertations, Academic -- UF
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Environmental Engineering Sciences thesis, M.E.
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government publication (state, provincial, terriorial, dependent)   ( marcgt )
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Abstract:
Several mathematical models or source strength functions have been proposed to describe the temporal dissolution of dense nonaqueous phase liquids in groundwater. Comparing functions to information in historical data sets at contaminated sites may produce reliable estimates of a site?s source zone dissolution parameters that can be used as tools in planning future site management. This research effort was aimed at developing protocols for using current mass discharge data from transects of concentration data and from pumping activities in the pursuit of estimating parameters of source strength functions at field sites to effectively guide site management decisions. An exhaustive search algorithm was programmed in FORTRAN to locate the best fit parameters for two of the proposed source dissolution models linked to a one-dimensional advection dispersion equation. The code was validated with a synthetic data set generated using MODFLOW and RT3D. The code was then applied to mass discharge data at four field sites and concentration data from a pumping well on one field site. It was found that the methods could be successfully applied to field sites but that the equations contained too many sensitive fitting parameters to confidently isolate a unique set of best fit parameters. Future work should look at ways minimizing the number of fitting parameters. These protocols will help advance the use of source strength functions as a measure used by those making site management decisions.
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In the series University of Florida Digital Collections.
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by Rachel E Donahue.
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Thesis (M.E.)--University of Florida, 2011.
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Adviser: Annable, Michael D.
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ESTIMATINGSOURCESTRENGTHPARAMETERSATDNAPLCONTAMINATEDFIELDSITESUSINGHISTORICALTRANSECTANDPUMPINGDATAByRACHELE.DONAHUEATHESISPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFMASTEROFENGINEERINGUNIVERSITYOFFLORIDA2011

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c2011RachelE.Donahue 2

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Tomymotherandfather 3

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ACKNOWLEDGMENTS ThisresearchwasfundedbytheStrategicEnvironmentalResearchandDevelopmentProgram(SERDP)(ProjectNumberER-1613).SERDPistheDepartmentofDefense'senvironmentalscienceandtechnologyprogram.TheviewsandconclusionsexpressedhereinarethoseoftheauthorandarenotintendedtorepresentthoseoftheU.S.Governmentoritsagencies.IthankSERDPforthenancialsupportnecessarytocarryoutthisresearch.IthanktheUniversityofFloridaHigh-PerformanceComputingCenterforprovidingcomputationalresourcesandsupportthathavecontributedtotheresearchresultsreportedwithinthispaper.Ithankmysupervisorycommitteechairman,Dr.MichaelAnnable,forhelpingmenavigategraduateschoolaswellashisvaluableexpertiseandguidanceduringthisresearcheffort.IwouldalsoliketothankmycommitteemembersDrs.JamesJawitzandKirkHateldfortheirtimeandcritique.IextendaspecialthankstoBrandonWoodforprovidingtechnicalsupportthroughoutthisresearcheffort.IthankallmyteachersattheUniversityofFloridafortheknowledgetheyhavepassedontomeandthenewskillstheyhaveinstilledinme.Lastbutnotleast,IthankmyMother,Father,brother,andsisterfortheirunconditionalloveandencouragementandmyfriendsfortheirsupportandunderstanding. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 7 LISTOFFIGURES ..................................... 9 ABSTRACT ......................................... 11 CHAPTER 1INTRODUCTION ................................... 12 2BACKGROUNDINFORMATION .......................... 15 2.1SourceStrengthFunctions .......................... 15 2.1.1PowerLawModel ............................ 16 2.1.2EquilibriumStreamTubeModel .................... 17 2.1.3InitialMassandEquilibriumStreamTubeModel ........... 18 2.1.4ParkerandParkModel ......................... 19 2.1.5RationalModel ............................. 20 2.2ContaminantTransportEquations ...................... 21 2.3MassDischargeandTransects ........................ 23 2.4AnalysisofSourceStrengthFunctions .................... 24 3SITESELECTIONPROCESS ........................... 26 3.1SiteCriteria ................................... 26 3.2CandidateSites ................................. 26 3.3SelectedSites ................................. 27 3.3.1HillAFB,Utah,USA .......................... 27 3.3.2NASJacksonville,Florida,USA .................... 28 3.3.3EdinburoughSite,Adelaide,Australia ................. 29 3.3.4CalfPasturePoint,RhodeIsland,USA ................ 30 3.3.5HangarK,CapeCanaveral,Florida,USA .............. 30 4CODEDEVELOPMENT ............................... 38 4.1GeneralCode .................................. 39 4.1.1AlgorithmSelection ........................... 39 4.1.2ExhaustiveSearchFramework .................... 40 4.1.2.1SourcezonepumpingtwithPLmodel .......... 40 4.1.2.2PumpingmethodwithESTmodel ............. 41 4.1.2.3TransectmethodwithPLandESTmodel ......... 41 4.1.2.4Objectivefunctions ...................... 43 4.2CodeValidation ................................. 43 5

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4.2.1ValidationwithaSyntheticTemporalDataSet ............ 44 4.2.2ValidationwithSpatialData ...................... 48 4.2.2.1Validationwithasyntheticspatialdatasetatasiteageof25% ............................ 48 4.2.2.2Validationwithasyntheticspatialdatasetatasiteageof50% ............................ 50 4.2.2.3Validationwithasyntheticspatialdatasetatasiteageof75% ............................ 50 4.2.3InvestigationintotheImportanceofSpatialResolutionoftheData 52 4.2.4InvestigationintotheImportanceofLocationofLimitedDataSets 54 4.3DifferencesbetweenMT3DSolutionsandAnalyticalSolutions ...... 55 5RESULTSANDDISCUSSION ........................... 58 5.1HillAFB ..................................... 58 5.1.1FittoConcentrationTimeSeries ................... 58 5.1.2FittoCumulativeMassRemovedData ................ 58 5.1.3FittoCumulativeMassRemovedDatawithRestrictedSourceVolume ................................. 61 5.1.4FittoTruncatedCumulativeMassRemovedData .......... 61 5.1.5Sensitivity ................................ 64 5.2NASJacksonville ................................ 64 5.3EdinburoughSite ................................ 66 5.4CalfPasturePoint ............................... 66 5.5HangarKEast ................................. 69 5.6HangarKWest ................................. 71 5.7SimLab ..................................... 73 5.8LimitingtheNumberofFittingParameters .................. 74 5.8.0.1EdinburoughSite ...................... 74 5.8.0.2HangarKWest ........................ 78 6SUMMARYANDFUTURERESEARCH ...................... 80 APPENDIX AHILLAFBDATA .................................... 83 BCOMPUTERCODES ................................ 86 REFERENCES ....................................... 113 BIOGRAPHICALSKETCH ................................ 116 6

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LISTOFTABLES Table page 3-1CalculatedMassDischargeatNASJacksonville ................. 34 3-2CalculatedMassDischargeatEdinburoughSite,Adelaide,Australia ...... 35 3-3CalculatedMassDischargeatCalfPasturePoint,RhodeIsland ......... 36 3-4CalculatedMassDischargeatHangarKEast ................... 36 3-5CalculatedMassDischargeatHangarKWest .................. 37 4-1BestFitPLModelParametersusing20SyntheticTemporalMassDischargeDataPoints ...................................... 46 4-2BestFitESTModelParametersusing20SyntheticTemporalMassDischargeDataPoints ...................................... 46 4-3BestFitPLModelParametersusing3SyntheticTemporalMassDischargeDataPoints ...................................... 47 4-4BestFitESTModelParametersusing3SyntheticMassDischargeDataPoints 48 4-5BestFitPLModelParametersusing20SyntheticSpatialDataPointsatanAgeof25% ...................................... 49 4-6BestFitPLModelParametersusing3SyntheticSpatialDataPointsatanAgeof25% ......................................... 49 4-7BestFitParametersusing20SyntheticSpatialDataPointsatanAgeof50% 50 4-8BestFitESTModelParametersusing20SyntheticSpatialDataPointsatanAgeof50% ...................................... 51 4-9BestFitPLModelParametersusing3SyntheticSpatialDataPointsatanAgeof50% ......................................... 51 4-10BestFitESTModelParametersusing3SyntheticSpatialDataPointsatanAgeof50% ...................................... 51 4-11BestFitParametersusing20SyntheticSpatialDataPointsatanAgeof75% 53 4-12BestFitParametersusing3SyntheticSpatialDataPointsatanAgeof75% .. 53 4-13BestFitParametersusingVariousDataResolutionwitha)]TJ /F1 11.955 Tf 10.1 0 Td[(of0.2atanAgeof25% ......................................... 54 4-14BestFitPLModelParametersusingCombinationsof3SyntheticSpatialDataPoints ......................................... 54 7

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4-15BestFitPLModelParametersusingCombinationsof2SyntheticSpatialDataPoints ......................................... 56 5-1OptimizedSSFParametersatHillAFBusingConcentrationData ........ 58 5-2OptimizedSSFParametersusingCumulativeMassRemovedData ....... 61 5-3OptimizedSSFParametersusingCumulativeMassRemovedDatawithaSetSourceVolume .................................... 61 5-4OptimizedSSFParametersusingTruncatedCumulativeMassRemovedData 64 5-5AdditionalYearsofPumpingtoreachMCLwithPLModeltswithCOEabove0.95 .......................................... 65 5-6OptimizedSSFParametersusingNASJacksonvilleData ............ 66 5-7OptimizedSSFParametersusingEdinburoughData ............... 69 5-8OptimizedSSFParametersusingCalfPasturePointData ............ 69 5-9OptimizedSSFParametersusingHangarKEastData .............. 71 5-10OptimizedSSFParametersusingHangarKWestData ............. 72 5-11OptimizedSSFParametersusingEdinburoughDatawhenThreeParametersareFixed ....................................... 78 5-12OptimizedSSFParametersusingHangarKWestDatawhenThreeParametersareFixed ....................................... 79 A-1HillAFBPumpingData ............................... 83 8

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LISTOFFIGURES Figure page 3-1WellandTransectLocationsatNASJacksonville( CH2MHill 2008 ) ....... 31 3-2WellandTransectLocationsatEdinburoughSite,Adelaide,Australia( Basuetal. 2009 ) ...................................... 32 3-3WellandTransectLocationatCalfPasturePoint,RhodeIsland( TetraTech 2008 ) ......................................... 32 3-4DPTLocationsatHangarK( COREEngineeringConstruction,Inc. 2009 ) .. 33 3-5WellLocationsatHangarK( BEMSystems,Inc. 2002 ) ............. 33 4-1SyntethicDataSSFs ................................. 45 4-2SyntheticTemporalDataat40Meters ....................... 47 4-3SyntheticSpatialDataataSiteAgeof25% .................... 49 4-4SyntheticSpatialDataataSiteAgeof50% .................... 52 4-5SyntheticSpatialDataataSiteAgeof75% .................... 53 4-6CombinationsofThreeDataPointsfromPLModel ................ 55 4-7CombinationsofTwoDataPointsfromPLModel ................. 55 4-8ComparisonbetweentheMT3Dandanalyticalsolutions ............. 56 4-9AnalyticalsolutionsusingtheBestFitandCorrectPLModelParameters .... 57 5-1HillAFBConcentrationFitsWithPumpingDatafrom1999-2009 ........ 59 5-2HillAFBFitwithCumulativeMassRemovedDatafromPumpingActivitiesbetween1999-2009 ................................. 60 5-3HillAFBCumulativeMassRemovedFitwithPumpingDatafrom1999-2009andRestrictedSourceVolume ........................... 62 5-4HillAFBFitwithCumulativeMassRemovedDatafromPumpingActivitiesbetween2004to2010 ................................ 63 5-5PossiblePLModelFitsatHillAFB ......................... 65 5-6ModeledMassDischargeatNASJacksonvillein2002UsingExhaustiveSearchResults ........................................ 67 5-7ModeledMassDischargeatEdinburoughin2006UsingExhaustiveSearchResults ........................................ 68 9

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5-8ModeledMassDischargeatCalfPasturePointUsingExhaustiveSearchResults 70 5-9ModeledMassDischargeatHangarKEastUsingExhaustiveSearchResults 72 5-10ModeledMassDischargeatHangarKWestUsingExhaustiveSearchResults 73 5-11MorrisSensitivityAnalysesforthePLModel ................... 75 5-12MorrisSensitivityAnalysesfortheESTModel ................... 76 5-13ModeledMassDischargeatEdinburoughin2006withThreeFixedParameters 77 5-14ModeledMassDischargeatHangarKWestwithThreeFixedParameters ... 79 10

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AbstractofThesisPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofMasterofEngineeringESTIMATINGSOURCESTRENGTHPARAMETERSATDNAPLCONTAMINATEDFIELDSITESUSINGHISTORICALTRANSECTANDPUMPINGDATAByRachelE.DonahueAugust2011Chair:MichaelAnnableMajor:EnvironmentalEngineeringSciencesSeveralmathematicalmodelsorsourcestrengthfunctionshavebeenproposedtodescribethetemporaldissolutionofdensenonaqueousphaseliquidsingroundwater.Comparingfunctionstoinformationinhistoricaldatasetsatcontaminatedsitesmayproducereliableestimatesofasite'ssourcezonedissolutionparametersthatcanbeusedastoolsinplanningfuturesitemanagement.Thisresearcheffortwasaimedatdevelopingprotocolsforusingcurrentmassdischargedatafromtransectsofconcentrationdataandfrompumpingactivitiesinthepursuitofestimatingparametersofsourcestrengthfunctionsateldsitestoeffectivelyguidesitemanagementdecisions.AnexhaustivesearchalgorithmwasprogrammedinFORTRANtolocatethebesttparametersfortwooftheproposedsourcedissolutionmodelslinkedtoaone-dimensionaladvectiondispersionequation.ThecodewasvalidatedwithasyntheticdatasetgeneratedusingMODFLOWandRT3D.Thecodewasthenappliedtomassdischargedataatfoureldsitesandconcentrationdatafromapumpingwellononeeldsite.Itwasfoundthatthemethodscouldbesuccessfullyappliedtoeldsitesbutthattheequationscontainedtoomanysensitivettingparameterstocondentlyisolateauniquesetofbesttparameters.Futureworkshouldlookatwaysminimizingthenumberofttingparameters.Theseprotocolswillhelpadvancetheuseofsourcestrengthfunctionsasameasureusedbythosemakingsitemanagementdecisions. 11

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CHAPTER1INTRODUCTIONThereareoftensubstantialhistoricalgroundwaterqualitydatasetsassociatedwithdensenonaqueousphaseliquid(DNAPL)contaminatedsites.Thesedatasetsaccumulatethroughpastsitecharacterizationeffortsusuallycarriedoutforthepurposeofremedialinvestigationsorregulatorycompliance.Sitemanagersandconsultantsmustutilizethesedatasetstoguidefuturesitecharacterizationeffortswiththeultimategoalofmakingdecisionsaboutfuturesitemanagement.Sourcezonedissolutioncharacteristicscanprovidevaluableinformationwhenchoosingasitemanagementapproach.Thesourcezonedissolutionatasiteisindicativeofthelongevityofthesource,therateatwhichtheplumewillprogress,and,consequently,thepotentialoftheplumetohavedeleteriouseffectstohumanhealthortheenvironment.Athoroughgraspoftherelationshipbetweensourcezonedissolutionandplumeresponsescanalsohelpdeterminetheefcacyofsourcezoneremediationonmitigatingthecontaminantplume.Thus,knowledgeofasite'ssourcezonedissolutioncharacteristicscanbecrucialtomakingsound,economicalrisk-basedremediationdecisions.Severalmathematicalsourcestrengthfunctionshavebeenproposedintheliterature.ThesefunctionsmodelDNAPLsourcezonedissolutionthroughtimeusingseveralparameters( Faltaetal. 2005b ; Jawitzetal. 2005 ).Ifthesefunctionscanbecomparedtoinformationinhistoricaldatasetsatcontaminatedsitestoproducereliableestimatesofasite'ssourcezonedissolutionparameters,thesourcestrengthfunctionscanbekeytoolsinplanningfuturesitemanagement.Thisresearchisaimedatdevelopingprotocolsthatcanbeusedbysitemanagersforanalyzingcurrentsitedataandplanningbenecialadditionaldatacollectioninthepursuitofestimatingparametersofsourcestrengthfunctionsateldsitesaccuratelyenoughtoeffectivelyguidesitemanagementdecisions.Thisisoneofseveralobjectivesofalargerprojectaimedatdevelopingeld-scaleapproachesthatDNAPLsite 12

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managerscanemploytolinksitecharacterization,prediction,andeffectivedecisionmaking.Forthisproject,vedifferentmethodshavebeenidentiedtocullvaluableinformationfromsitedataandanalyzetheinformationinanefforttotittoexistingsourcestrengthfunctionsandproduceestimatesoffunctionparameters.Themethodsaredescribedbelow: 1. GlobalFit-besttmodelparametersfortheentiresiteareestimatedusingallavailablespatialandtemporalconcentrationdata. 2. IndividualWellFit-besttparametersforeachindividualsamplingwellareestimatedusingtemporaldatafromeachwell. 3. PumpingWellFit-besttparametersfortheentiresiteareestimatedusingtemporalconcentrationtimeseriesfrompumpingactivitiesatthesite. 4. SpatialTransects-besttparametersfortheentiresiteareestimatedusingaseriesofspatialmassdischargevaluescalculatedusingconcentrationdatafromwellsformingcontrolplanesthatareperpendiculartothepredominantowdirection. 5. TemporalTransects-besttparametersfortheentiresiteareestimatedusingaseriesoftemporalmassdischargevaluescalculatedusingtemporalconcentrationdatafromwellsformingacontrolplanethatisperpendiculartothepredominantowdirection.Acombinationofbothspatialandtemporaltransectscanbeusedatsiteswherebothspatialandtemporaltransectdataisavailable.Particularmethodsaremoreappropriatethanothersfordifferentsitesdependingonwhattypeofinformationisalreadyavailable.Therstobjectiveofthisresearchwastodevelopprotocolsforemployingthepumpingwellt,spatialtransects,andtemporaltransectsmethodsateldsiteswithhistoricaldata.Asecondaryobjectivewasthesuccessfulapplicationofthedevelopedprotocolsateldsites.Foreachmethodtobeusedbysitemanagerstheprotocolshadtoincludeanapproachtodeterminemethodapplicabilitytoasiteand,ifapplicable,togatherthenecessaryinformationfromthesite'sdatasets.Next,theprotocolspresentaprocesstodeterminethebestestimateofthesourcestrengthparameters.AsensitivityoftheapproachtodifferentvaluesforthekeyparametersineachSSFwasalsoneeded 13

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inordertotoverifytheefcacyoftheprotocolsaswellasthereliabilityofeachbesttparameterestimate.Theseprotocolshelpadvancetheuseofsourcestrenghtfunctionsasameasureusedbythosemakingsitemanagementdecisions.Additionally,themethodscanbeusedtoguidefuturesitecharacterizationwiththeaimofquantifyingandreducingthetsensitivityassociatedwithsourcestrengthparameterestimatesfromtransectorpumpingdata. 14

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CHAPTER2BACKGROUNDINFORMATION 2.1SourceStrengthFunctionsDNAPLsareliquidsthatareheavierthanwater.Wheninthepresenceofwateratconcentrationsabovetheirsolubilitylimits,DNAPLsseparateandsink.TwocommonDNAPLsareperchloroethene(PCE)andtrichloroethene(TCE).PCEandTCEwereproducedonalargescaleintheUnitedStatesfollowingWorldWarII.TCEwasusedtodegreasemachineryandPCEwasusedinthedrycleaningprocess.Duetopoorhandlingandinadequatedisposalpractices,theywereoftenreleasedintotheenvironment( McCarty 2010 ).Afterinltratinggroundwatersystems,thechemicalsformpoolsabovelowconductivityzones.Naturalgradientowcauseswatertoowthroughthesourcezonewhereportionsofthesourcezonemassdissolveandaretransportedwiththegroundwaterow.Thedissolvedcontaminantformsadowngradientplume.Therateofmassleavingthesourcezoneisreferredtoasux.Fluxrepresentsamassperareapertime.RaoarguedthattheefcacyofDNAPLsourcezoneremediationshouldbebasedoncontaminantuxreductionsratherthancontaminantconcentrationreductions( 2001 ).AsourcezoneremediationeventmaynotreduceconcentrationsinthesourcezonetoregulatorylimitsbutmayalterthehydrodynamiccontactwiththeremainingDNAPLmassenoughtoreducethesourcezonemassuxtoacceptablelevels.RaoanalyzedthirtyparticletrackingsimulationsinheterogeneousoweldsandfoundmassuxleavingDNAPLsourcezonestotapowerlawfunction.Thebasicpowerlawfunctionproposedisshownin 2 whereYisfractionalDNAPLuxreduction,XisfractionalDNAPLmassreduction,andisanempiricalparameterthatrepresentuxreductionefciency.Fluxreductionefciencyisafunctionoftheheterogeneityoftheoweldandthesourcearchitecture. Y=X1 (2) 15

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Thevalueofcanbeusefulincomparingtheeconomicsofremediationoptionsaswellasprojectingsourcezonedissolutionintothefuture.Equation 2 isalsoapplicabletosourcedissolutionbynaturalgradientowalone.ThefollowingmodelsarebuiltonEquation 2 andrepresentmoredetailedmathematicalmodelsdescribingsourcezonedissolution. 2.1.1PowerLawModelFaltaetal.describedsourcezonedissolutionwithapowerlaw(PL)model( 2005b ).Thegeneralequationforthismodelisasfollows, Cs(t)=Co M)]TJ /F9 7.97 Tf -.93 -6.41 Td[(o)]TJ /F5 11.955 Tf 9.3 0 Td[(VdAC0 sM)]TJ /F9 7.97 Tf -.93 -6.41 Td[(o+M1)]TJ /F10 7.97 Tf 6.58 0 Td[()]TJ /F9 7.97 Tf -11.95 -7.89 Td[(o+VdACo sM)]TJ /F9 7.97 Tf -.93 -6.41 Td[(oe()]TJ /F12 7.97 Tf 8.26 0 Td[()]TJ /F10 7.97 Tf 6.59 0 Td[(1)st)]TJ ET q .359 w 369.78 -200.96 m 382.48 -200.96 l S Q BT /F7 5.978 Tf 369.78 -206.08 Td[(1)]TJ /F7 5.978 Tf 5.75 0 Td[()]TJ /F1 11.955 Tf 61.24 -11.06 Td[((2)where,Csistheconcentrationleavingthesourcezoneattimet,Coistheinitialconcentrationleavingthesourcezone,Moistheinitialsourcezonemass,Aistheareaofthecross-sectionalcontrolplaneperpendiculartothegroundwaterowdirection,VdistheDarcyvelocity,isarateconstantthataccountsforabioticandbioticdegradation,and)]TJ /F1 11.955 Tf 10.1 0 Td[(isanempiricalparameterthatcontrolstherateofdecreaseinsourcezonemassdischargeovertime.ThePLmodelistheonlysourcestrengthfunctionconsideredherethatincludesadegradationrate.Whennodegradationisassumed,canbesetequaltozeroandEquation 2 reducestoEquation 2 Cs(t)=Co M)]TJ /F9 7.97 Tf -.93 -6.4 Td[(o()]TJ /F2 11.955 Tf 14.31 0 Td[()]TJ /F3 11.955 Tf 11.96 0 Td[(1)VdACo M)]TJ /F9 7.97 Tf -.94 -6.4 Td[(ot+M1)]TJ /F10 7.97 Tf 6.58 0 Td[()]TJ /F9 7.97 Tf -11.95 -7.89 Td[(o)]TJ ET q .359 w 330.15 -441.22 m 342.85 -441.22 l S Q BT /F7 5.978 Tf 330.15 -446.33 Td[(1)]TJ /F7 5.978 Tf 5.76 0 Td[()]TJ /F1 11.955 Tf 100.86 -11.06 Td[((2)Twomathematicallyspecialcasesofthismodeloccur.When)]TJ /F1 11.955 Tf 10.1 0 Td[(=1,themodelbecomes Cs(t)=Coe)]TJ /F14 5.978 Tf 5.75 0 Td[(VdACo Mot(2)When)]TJ /F1 11.955 Tf 10.1 0 Td[(=0.5,themodelreducesto Cs(t)=Co)]TJ /F5 11.955 Tf 13.15 8.09 Td[(VdAC2o 2Mot(2) 16

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Equations 2 2 2 canbemanipulatedtogivemassleftinthesourceasafunctionoftime.ThisresultsinEquations 2 and 2 M(t)=()]TJ /F2 11.955 Tf 14.32 0 Td[()]TJ /F3 11.955 Tf 11.95 0 Td[(1)VdACo M)]TJ /F9 7.97 Tf -.93 -6.41 Td[(ot+M1)]TJ /F10 7.97 Tf 6.59 0 Td[()]TJ /F9 7.97 Tf -11.96 -7.89 Td[(o)]TJ ET q .359 w 319.02 -56.72 m 331.72 -56.72 l S Q BT /F7 5.978 Tf 319.02 -61.84 Td[(1)]TJ /F7 5.978 Tf 5.76 0 Td[()]TJ /F1 11.955 Tf 112 -11.06 Td[((2)When)]TJ /F1 11.955 Tf 6.77 0 Td[(=1,theequationforsourcemassasafunctionoftimebecomes 2 M(t)=Moe)]TJ /F14 5.978 Tf 7.78 4.62 Td[(VdACo Mot(2)UponexaminationofEquations 2 and 2 ,itwasfoundthatEquations 2 isonlyreliableat)]TJ /F6 11.955 Tf 11.81 0 Td[(>1.Themostaccurateapproachtoevaluatingcaseswhere)]TJ /F2 11.955 Tf 11.81 0 Td[(1andthereisnodegradationistouse 2 andsetstoavalueof1x10)]TJ /F10 7.97 Tf 6.59 0 Td[(7. 2.1.2EquilibriumStreamTubeModelTheequilibriumstreamtube(EST)modelisaLagrangianmodeldevelopedbyJawitzetal.andbasedontheconceptofvisualizingthesourcezoneasasystemofnonintersectingstreamtubescontainingadistributionofDNAPLsaturationsandtraveltimesrequiredtocleanagiventube( 2003 ).ThemainequationfortheESTmodelis Cf(T)=fcCs(1)]TJ /F5 11.955 Tf 11.95 0 Td[(p())(2)where,Tisthenumberofporevolumesthathavepassedthroughthesourcezone,Cf(T)istheux-averagedconcentrationatacontrolplaneattheendofthesourcezoneafterTporevolumeshavepassedthroughthesource,fcistheinitialfractionofstreamtubescontainingDNAPL,andp()isthecumulativeprobabilitydistributionfunctionof.isthereactivetraveltimeandisfoundusingEquation 2 =Kwt^S(2)InEquation 2 ,KwisequaltotheratioofthedensityoftheDNAPLtotheaqueoussolubilityoftheDNAPL,tisthenonreactivetraveltime,and^Sisequaltothetrajectory-integratedDNAPLcontent.Thecumulativeprobabilitydistributionfunction,assumingislog 17

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normallydistributed,isdenedasfollows, p()=1 2+1 2erflnT)]TJ /F6 11.955 Tf 11.96 0 Td[(ln lnp 2(2)where,lnisthemeanofthelogtransformedvariableandlnisthestandarddeviationofthelogtransformedvariable(Basuetal,2008).TheporevolumesfortheESTModelequationsarecalculatedwith 2 pv=vt sl(2)where,tistimeandslissourcelength. 2.1.3InitialMassandEquilibriumStreamTubeModelInthewaytheESTModelispresentabove,MoisnotexplicitasitisinthePLModel.TheMovaluecanbedeterminedbyoneofthreeapproaches.TheinitialmasscanbedeterminedbyintegrationofEquation 2 .OnewaytointegratethisfunctionistousetheQAGIfunctionintheQUADPACKpackageforFORTRANwhichnumericallyintegratesagivenfunctionfromzerotoininity( Piessensetal. 1983 ).ThesecondapproachistousestepwiseintegrationtoobtaintheareaundertheconcentrationtimeseriescalculatedwithEquation 2 .Lastly,themasscanbedeterminedusingtherstmomentsofthenonreactivetraveltimeandbSdistributions.TodothisEquation 2 wasusedtogettherstmomentofbS( Jawitzetal. 2005 ). m1=mt1+Kwmt1mbS1(2)where,m1istherstmomentof,mt1istherstmomentoft,mbS1istherstmomentofbS,andrepresentsthecorrelationbetweenbSandt.Nocorrelationisassumedsoequals1.mt1isassuemdtoequaltherespresentedtraveltimethroughthesourceandhasunitsoftime.m1canbecalculatedwiththerstmomentequationshowninEquation 2 m1=expln+2ln 2(2) 18

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mbS1isequaltotheaveragesaturation, S.UsingtherelationshipsshowninEquations 2 2 ,and 2 ScanbeusedtocalculateDNAPLsaturation( SN),thenvolumeofDNAPL(VN),andlastly,Mo. SN= S 1)]TJ ET q .478 w 255.42 -83.32 m 263.46 -83.32 l S Q BT /F5 11.955 Tf 255.42 -93.3 Td[(S(2) SN=VN V(2)where,Visthevolumeofthesourcezone. Mo=VN(2)whereisthedensityofthecontaminant.Allthreeofthesemethodsweretestedusingasyntheticdatasetwithalnof4.3,lnof1.2,f.c.of1.0,avelocityof0.1m/dayandaslof3m.ThenumericalintegrationapproachgaveaMovalueof499.66kg.StepwiseintegrationofthefuncitongaveaMovalueof500.66kg.Themomentsapproachgaveavalueof445.9kg.AllMovaluesfortheESTModelinthethispaperwerecalculatedbynumericalintegrationusingQAGIbecausethisapproachgaveasimilaranswertothestepwiseintegrationapproachbutwaseasiertoperform. 2.1.4ParkerandParkModelParkerandParkpresentedaeld-scalemasstransferfunctionbyupscalinghigh-resolution,three-dimensionalsimulationsofDNAPLsourceregionsusedtostudysourcezonedissolutionkinetics( 2004 ).ThemodelusedaDNAPLpercolationmethodtosimulatethedistributionofTCEreleasedina10x10x10metersourcezonewithalognormallydistributedhydraulicconductivityeld.Agroundwaterowandcontaminanttransportmodelwasthenusedtosimulatetheplume'sprogression.Themasstransferfunctioniscreatedbyreplacingtheheterogeneoussourcezonewithahomogeneoussourcezoneofidenticaldimensionsandapplyingthesameaveragehydraulicux.Assumingdissolutionissteadystate,ifthegroundwatervelocityisheldconstant,the 19

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pseudo-steadystateconditionscanbedescribedbyEquation 2 whereqistheaverageDarcyvelocityandeisthemasstransfercoefcientforDNAPLdissolutionwhichisttingparameterinthismodel. q@C @x=)]TJ /F6 11.955 Tf 9.3 0 Td[(e(Ceq)]TJ /F3 11.955 Tf 13.54 2.65 Td[(C)+qd2C dx2(2)Iftheinuentconcentrationissettozero,Equation 2 canbesolvedtogivetheclosedformsolutionshowninEquation 2 whereCout=C(L). Cout Ceq=1)]TJ /F5 11.955 Tf 11.96 0 Td[(exp(L 2L 1)]TJ /F11 11.955 Tf 11.95 16.86 Td[(1+4eL q1=2!)(2)Equation 2 reducestoEquation 2 when/Lislessthan0.1whichisgenerallythecase(when/Lislessthan0.1,sourcedissolutionisdominatedbyadvection). Cout Ceq=1)]TJ /F5 11.955 Tf 11.96 0 Td[(expeL q(2)Equation 2 cannowbettohistoricaluxdatafromasitetodetermineanestimateofevalueatthesite.Thettingparameter,e,isrepresentedmathematicallyinEquation 2 e=oDo d2w wDo1=2qrwDo w1(Sor)2(2)InEquation 2 ,disthehydraulicdiameter,isporosity,SoristheresidualDNAPLsaturation,andbasedonlaboratorystudies,o=12,1=0.75,and2=0.6( ParkerandPark 2004 ). 2.1.5RationalModelAnothermodelhasrecentlybeendevelopedthatdrawsfromthepowerfunctionmodels,suchasthePLModel,andtheESTModel.Theresultingmodel,theRationalModel,andhasbeendevelopedonanempiricalbasis( Pattersonetal. 2011 ).ForagivenaveragesaturationandKw,Jawitzfoundthatthepowerfunctionrelationshipswereonlyapplicabletosituationswithln0.7( Jawitzetal. 2005 ).Whenln0.7,theobservedrelationshipfollowedEquations 2 and 2 .InEquation 2 ,RjandRm 20

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representthefractionalreductionsinuxandmass,respectively. =1.31(ln)1.22(2) Rj=(Rm)1=(2)Whenlnexceeds0.7,anotherempiricalrationalfunctionwaspresentedtobetterrepresenttherelationshipbetweenmassreductionandmassuxreduction(Jawitzetal2005).ThisrelationshipisshowninEquations 2 and 2 =1.03(ln)4.05(2) Rj=Rm(1+) 1+Rm(2)Thelimitationoftherationalmodelisthatitcannotbemanipulatedtorepresentaclosedformsolutionformassuxasafunctionoftime. 2.2ContaminantTransportEquationsInacompanionpaper,FaltapresentedEquation 2 whichcanbeusedtosolvethecontaminantconcentrationatanypointintheplumeasafunctionoftime( 2005a ).Equation 2 isanadvectiondispersioncontaminanttransportmodelthatutilizesasourcestrengthfunctionasauxboundarycondition. C(x,y,z,t)=fy(y)fz(z)Zt0Cs(t)]TJ /F6 11.955 Tf 11.95 0 Td[()@B(x,) @d(2)InEquation 2 ,Cs(t)]TJ /F6 11.955 Tf 12.67 0 Td[()canbefoundwithanyexistingclosedformsolutionofasourcestrengthfunctionand fy(y)=1 2 erf(y+Y 2 2p yx))]TJ /F5 11.955 Tf 11.95 0 Td[(erf(y)]TJ /F9 7.97 Tf 13.15 4.7 Td[(Y 2 2p yx)!(2) fz(z)=1 2erfz+Z 2p zx)]TJ /F5 11.955 Tf 11.96 0 Td[(erfz)]TJ /F5 11.955 Tf 11.95 0 Td[(Z 2p zx(2) 21

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@B(x,t) @t=v v+uRx+ut 2tp xvRtexpv)]TJ /F5 11.955 Tf 11.96 0 Td[(u 2xv)]TJ /F3 11.955 Tf 13.15 8.09 Td[((Rx)]TJ /F5 11.955 Tf 11.95 0 Td[(ut)2 4xvRt+v v)]TJ /F5 11.955 Tf 11.96 0 Td[(uRx)]TJ /F5 11.955 Tf 11.95 0 Td[(ut 2tp xvRtexpv+u 2xv)]TJ /F3 11.955 Tf 13.15 8.09 Td[((Rx+ut)2 4xvRt+v 2pxRx)]TJ /F5 11.955 Tf 11.95 0 Td[(ut 2tp xvRtexpx x)]TJ /F6 11.955 Tf 13.15 8.08 Td[(pt R)]TJ /F3 11.955 Tf 13.15 8.08 Td[((Rx+ut)2 4xvRt)]TJ /F11 11.955 Tf 11.95 16.85 Td[(v 2Rxexpx x)]TJ /F6 11.955 Tf 13.15 8.09 Td[(pt RerfcRx+vt 2p xvRt(2)InEquation 2 and 2 ,YandZrepresentthewidthanddepthofthesourcezone,respectively,andyandzrepresentthetransverseandverticaldispersivities,respectively.InEquation 2 ,visthepore-watervelocity,Ristheretardationfactor,tisthetimesincerelease,xisthelongitudinaldispersivity,xisthedistancedowngradientfromthesource,andpisthesourcezonedecayrateconstantwithunitsofinversetime.Theparameterucanbecalculatedusingthefollowingrelationship. u=vr rpx v(2)Equation 2 canalsobesolvedforthecaseofnodegradation.Thefyandfztermsareunchangedbytheremovalofthedegradationterm;however,eliminatingdegradationchangesthepartialderivativeofB(x,t).ThevalueofpinEquation 2 cannotsimplybesetequaltozerotoeliminatedegradation;thiswouldcreateundenedtermsintheequation.Toeliminatedegradation,Equation 2 mustbeused. @B(x,t) @t=pexp)]TJ /F5 11.955 Tf 11.51 8.09 Td[(s2 4n8<:)]TJ /F5 11.955 Tf 9.3 0 Td[(v 2p n)]TJ /F5 11.955 Tf 14.96 8.09 Td[(RDs 4n3=2)]TJ /F5 11.955 Tf 35.35 8.09 Td[(v2 2RDq v2t RD)]TJ /F11 11.955 Tf 11.95 19.27 Td[(r v2t RDs2 4n2+vs 2n9=;)]TJ /F5 11.955 Tf 13.16 8.09 Td[(exp(q) 2v2 DRerfcm 2p n)]TJ /F11 11.955 Tf 11.96 16.85 Td[(1+q+v2t DRexp(q)pexp)]TJ /F3 11.955 Tf 9.29 0 Td[((m)2 4nv 2p n)]TJ /F5 11.955 Tf 17.76 8.08 Td[(RDm (4n3=2)(2)Equations 2 2 2 2 ,and 2 denetermsp,q,m,s,andnofEquation 2 ,respectively. p=1 p (2) 22

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q=vx D(2) m=(rx)+(vt)(2) s=(rx))]TJ /F3 11.955 Tf 11.95 0 Td[((vt)(2) n=Drt(2)Equation 2 wasderivedbytakingthepartialderivativewithrespecttotimeofEquation44inGroundwaterTransport:HandbookofMathematicalModels( Javandeletal. 1984 ).Equation44istheone-dimensionalowequationforadvective-dispersivesolutetransportwithnodegradation. 2.3MassDischargeandTransectsMassdischarge,Mdisgenerallymeasuredusingpointmeasurementsfromacontrolplanecomprisedofwellsthatlieperpendiculartothepredominantowdirection.Eachtransectcontainsanumberofwells,nwell.Eachwellmayhavemultipleverticalsamplinglocations,nver.Thisleadstoasetofkmeasurementslocationswherek=nwellnver.Foreachmeasurement,arepresentativeareaoftheaquifer,Ak,isassignedbasedonthedistancestothenearestwellsortheedgeofthecontrolplane.Next,themassdischargeowingthroughthetransectatthetimeofthemeasurementscanbecalculated.Massdischargecanbecalculatedusingdifferentequationsdependingontheinformationmeasuredateachlocation( KubertandFinkel 2006 ).IfthecontrolplaneismadeupofmonitoringwellsEquation 2 canbeused. Md=qDkXi=1(CkAk)(2)Ifthemeasuringlocationsinthecontrolplaneweresampledwithpassiveuxmeters,Equation 2 canbeused. Md=kXi=1(JkAk)(2)InEquation 2 ,Jkrepresentsmassuxatsamplelocationk. 23

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Whenconcentrationoruxdataareavailableforacontaminantanditsdaughterproducts,theconcentrationscanbeexpressedinequivalentsoftheparentcontaminantusingEquation 2 C1)]TJ /F9 7.97 Tf 6.58 0 Td[(Equivalents=C1 MW1+C2 MW2+C3 MW3+MW1(2)InEquation 2 ,C1istheparentcontaminant,andC2,C3,andsofortharetheconsecutivedaughterproducts.CandMWrepresenttheconcentrationandthemolecularweight,respectively,ofthechemicalspeciedinthesubscript. 2.4AnalysisofSourceStrengthFunctionsSeveralresearchershaveusedlaboratoryorcomputermodelstostudytheaforementionedmathematicalSSFs.Fureperformedfourdissolutionexperimentsintwo-dimensionalowcells.ThedissolutionproleswerethenmodeledusingtheESMandDaM.Bothwerefoundcapableofmodelingthesimpleexperiments.The^Sdistributionwasfoundtobethemaininuenceondissoutionbehavior.Velocityvariabilitywasfoundtoadjustthevariabilityaroundthisbehavior( 2006 ).BasuinvestigatedhowwellfourSSFsrepresentedsourcezonedissolutionusingUTCHEM.Thefourmodelinvestigatedwereanadvection-dispersionmodel(ADM),ESTModel,PLModel,andDamkohlerModel.AllmodelswerefoundtobeadequatesimpliedmodelsofDNAPLsourcezonedissolution.TheESTandADMmodelswerealmostidentical.TheleastaccuratemodelwasthePLModel( Basuetal. 2008 ).ParkersimulatedaTCEspill.Thespillwasmonitoredwith22wellsfor23years.Subsetsofthedatawereusedtocalibrateasourcemodel.Thelowestuncertaintywasfoundwhentheentireplumedataplusnearsourcedischargewereusedtocalibratethemodel.Estimatesfromcalibratingthemodelusingonlynearsourcedatawereassociatedwithhighuncertainty.Themodelwasmademorecomplexbyaddingadditionalsources.Thisdecreaseduncertaintyuptoapoint.Atacertainpointthe 24

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uncertaintyontheestimatescouldnotbeimprovedwithoutahigherqualitydataset( Parkeretal. 2010 ).ChenandJawitzperformedsurfactantoodsintwo-dimensionalowchambers.Usingthedatafromthesurfactantoods,itwasshownthatallsourcezones,regardlessofinitialarchitecture,convergetoastateinwhichfractionalreductionincontaminantuxequalsfractionalreductionsinmass( 2009 ). 25

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CHAPTER3SITESELECTIONPROCESS 3.1SiteCriteriaAlistofcandidatesiteswasproposed.ThecandidatesiteswerechosenbecausetheyweresiteswhereitwasknownthataquifershadbeencontaminatedwithDNAPLs.Nexttheavailablehistoricalassessmentsanddatasetsforthesiteswerereviewedtondsitesthathadthetypeofdatanecessarytocreateaconcentrationtimeseriesfrompumpingactivitiesortocalculateatleasttwotemporalorspatialmassdischargevaluesbasedonwelltransects.Whenlookingforwelltransectsatsites,thetransectsdidnothavetobeintentionallyplanned.Ifwellshadbeeninstalledcloseenoughtoformalineandsampleshadbeentakenfromthewellswithinayearofeachother,theconcentrationdatafromthewellswasassumedtorepresentasnapshotofthemassdischarge. 3.2CandidateSitesThefollowingisalistofthesiteswhosehistoricaldatasetswereinvestigatedbecausetheymetthecriteriaofbeingtheporousmediawithDNAPLcontaminatedgroundwater: 1. SagesDrycleaner,Florida,USA 2. LC-34CapeCanaveral,Florida,USA 3. HillAFBOU-3,Utah,USA 4. EGDYFt.Lewis,Washington,USA 5. NTCOrlandoSA17,Florida,USA 6. NASJacksonville,Florida,USA 7. NASPensacolaSWMU1(WWTP),Florida,USA 8. NSFIndianHeadSite57,Maryland,USA 9. HangarK,CapeCanaveral,Florida,USA 26

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10. MCASCherryPointOU1,NorthCarolina,USA 11. EdinburoughAdelaide,Australia 12. CoastGuardStationCapeCanaveral,Florida,USA 13. MCRDParrisIsland,SouthCarolina,USA 14. BelmontSite,Perth,Australia 15. ChevronSite,Richmond,California,USA 16. BPSite,LosAngeles,California,USA 17. NASAlamedaSite4,California,USA 18. CalfPasturePoint,RhodeIsland,USA 3.3SelectedSitesThesitesdescribedbelowwerechosenfromthecandidatesitesbecausetheassociatedhistoricaldatasetscontaineddatathatmetthecriteriaforthespatialtransect,temporaltransect,orpumpingwellmethod. 3.3.1HillAFB,Utah,USAHillAFBislocatedinNorthernUtah,vemilesSouthofthetownofOgden.Fromthe1940sto1968,itisassumedthattrichloroethene(TCE)wasusedasthemaindegreaseronthesite.From1968to1979,1,1,1-trichloroethane(TCA)wasprobablylargelysubstitutedforTCE.In1979theuseofTCEwasdiscontinuedatHillAFB.OperableUnit2(OU2)referstothelocationoftwounlinedtrencheswherechlorinatedsolventsweredisposedoffrom1967to1975.TCEwasthemainDNAPLdisposedofatthesitewithsmallamountsofTCAandtetrachloroethene(PCE).Thedisposalofthecontaminantsleadtothecontaminationoftheunderlyingaquifers( URS 2005 ).In1993,acontainmentwallwasbuiltaroundthetrenchesinordertocutoffdischargeofTCEandpreventfurtherplumedevelopment.Thecontainmentwallwasapproximately1,500feetinlengthandreacheddepthsof60to90feetbelowgroundsurface.Thewallenclosesapaleochannel.TheknownDNAPLlocationscorrespondto 27

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thelowestpointsofthepaleochannel.Theareaofthepaleochannelbelowtheaveragegroundwatertable,isestimatedtobe7,000cubicmeters.Asourcerecoverysystemoftwopumpandtreatwellswerealsoinstalledwithinthecontainmentwalltoremovethesourceandmaintainaninwardhydraulicgradient( URS 2005 ).Dataareavailableonthepumpingactivitiesfrom1999to2009.Thedataincludestwomonthlyreportedvalues,thevolumeofwaterpumpedforthemonthandoneTCEconcentrationsample.Thedatavaluescanbeusedtodeterminetheaverageowfor119monthsandaconcentrationleavingthesourcezoneforthatmonth.Therearetwomonthswithinthetenyearspaninwhichnopumpingoccurred.ThisdataisshowninthesecondandthirdcolumnsofTable A-1 foundinAppendix A alongwiththemassremovedpermonthandthecumulativemassremovedforeachmonth.Themassvalueswerecalculatedassumingaconstantconcentrationwasobservedforthewholemonth.Afterlookingatthedataset,threeofthereportedconcentrationscanbedisregardedbecausethereportedconcentrationsareatoraboveTCE'ssolubilitylimitof1.1g/L.Next,thedatasetwasreviewedtodetermineiftherewereanymonthsinwhichtheconcentrationismorethandoubletheconcentrationsfromthetwoconsecutivemonths;twoofsuchincidencesoccurred.FortheveconcentrationsthatwereeitherapproachingoraboveTCE'ssolubilitylimitoroverdoublethetwoconsecutivemonths,theconcentrationwasrecalculatedastheaverageofthetwoconsecutivemonths.TheadjusteddatasetisshowninTable A-1 inAppendix A 3.3.2NASJacksonville,Florida,USATheNavalAirStationatJacksonville,Florida(NASJax)wasdesignedin1938.Itspurposewastoprovideseaplanesupport.ItislocatedninemilessouthofJacksonville,FloridaalongthewesternbankoftheSt.JohnsRiver.AsNASJaxexpanded,thebankoftheSt.JohnsRiverwashydraulicallylledtomakemorelandavailable.NASJaxisnowapproximately3,800acres.OperableUnit3(OU3)withinNASJaxreferstotheareaalongthebankoftheSt.JohnsRiver.In1993,aScopingStudyFieldProgram 28

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(SSFP)wasperformedwhichinvolvedtakingsamplesbydirectpushtechnologyatthreedepthsalonga300-footgrid.TheSSFPidentiedtenareasofelevatedgroundwatercontaminationwithinOU3(1,000ug/L)( HardingLawsonAssociates 2008 ).OneoftheareaswasAreaCwhichwasfoundtobecontaminatedwithTCE.AreaCislocatedbetweentwoairplanehangars.InordertodesignaHRCinjectionatAreaCasamplingeventwascarriedoutusingdirectpushtechnologyfromJune18toJuly6,2001.Basedontheresultsofthesamplingevent,monitoringwelllocationswereproposed.ThemonitoringwellsformedtwotransectsreferredtoasB-B'andC-C'.C-C'is167metersdowngradientfromB-B'.AfterthemonitoringwellswereinstalledabaselinegroundwatermonitoringeventtookplaceonNovember5and6,2007( CH2MHill 2008 ).ThedatafromthebaselinemonitoringeventwereusedtocalculatetwospatialmassdischargevaluesusingEquation 2 usingthisaveragevelocityvalue.ThedatafromthebaselinegroundwatermonitoringeventalongwiththecalculatedmassdischargesareshowninTable 3-1 .Thedzvalueforeachwellwasapproximately1.5meters.Next,theerrorassociatedwiththeDarcyvelocity,concentrationvalues,andrectangularaquiferareasusedinEquation 2 werepropagatedtodeterminetheerrorassociatedwiththecalculatedmassdischargemeasurements.TheerrorassociatedwiththeDarcyvelocitywasassumedtobe30%.Allotherinputswereassumedtobesubjectto15%error. 3.3.3EdinburoughSite,Adelaide,AustraliaTheEdinburoughSiteisaTCEgroundwatercontaminatedsitelocatednearAdelaide,Australia.Thecontaminationiscausedbywastedisposalpracticesatthesitebetween1940and1970.Theonlyremediationworkcompletedatthesitewasexcavationtoabout6metersbelowgroundlevel.Duringexcavationapproximately4,000cubicmetersofcontaminatedsoilwasdisposedandcorrodeddrumswereremoved.In2006,PFMdeploymenttookplaceinthreephases.PhasesIandIIconsistedofplacingPFMinexistingwellsalonglongitudinaltransects.PhaseIIIinvolvedtheconstruction 29

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ofnewwellsintwotransversetransects.ThelocationofthewellsandtransectsaredepictedinFigure 3.3.5 ( Basuetal. 2009 ).ThedataforthesetransectsisshowninTable 3-2 alongwiththemassdischargescalculatedusingEquation 2 .Thesameerrorvaluesof30%forDarcyvelocityand15%fortheremainingvaluesinEquation 2 werepropagatedtogetanassociatederrorforeachmassdischargevalues. 3.3.4CalfPasturePoint,RhodeIsland,USAPreviouslyapartoftheNavalConstructionBattalionCenteratDavisville,CalfPasturePointisinNorthKingstown,RhodeIsland.Decontaminatingagentnon-corrosive(DANC)wasburiedatthesitesometimebetween1968and1974.DANCismainlymadeupof1,1,2,2,-tetrachloroethane(PCA)whichdegradesquicklytotricholoethene(TCE).Ithasbeenestimatedthat45,000kgofPCAwasburiedatthesite;however,thisestimateisassociatedwithhighuncertainty.Threewellsthatcanrepresentatransectwerechosenforlongtermmonitoring.ThesewellsareMW07-04D,MW07-05D,andMW07-17D(04D,05D,and17D).TheirlocationsareshowninFigure 3.3.5 .ThedatashowninTable 3-3 wasusedtocalculatemassdischargevalues.Equation 2 wasusedwithDarcyvelocitiesof0.11,5.12,and3.56m/yrfor04D,05D,and17D,respectively( TetraTech 2008 ).TheseDarcyvelocitiesarebasedonhydraulicconductivitiesmeasuredatthewellsandthehydrualicheadgradientsmeasuredatthesite.Thedyvaluesfor04D,05D,and17Dare30.85,31.62,and37.33meters,respectively.Allthreewellshaddzvaluesof3meters.ThemassdischargevalueforOctober2008wasremovedwhenanalyzingthedatabecauseitisanoutlier.Again,theerrorassociatedwitheachmassdischargewasdeterminedbypropagating30%errorfortheDarcyvelocitiesand15%errorfortheconcentrationandareavalues. 3.3.5HangarK,CapeCanaveral,Florida,USACapeCanaveralAirForceStationismadeupof15,800acresofbarrierislands.HangarKwasbuiltonthewesternsideofCapeCanaveralAirForceStationin1957.Itisnowthelocationofanapproximately180acreTCEplume.Theplumeencompasses 30

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othersmallercontaminantplumes.TheplumeisformedbytwosourcezoneslocatedontheEasternandWesternsideofthehangar.DPTsamplesfrom2002weretakenateachsource.ThelocationsareshowninFigure 3.3.5 .ThelocationsoftheDPTsamplesallowthreetransectstobeformeddowngradientofboththeEasternandWesternsourceareas.Groundwatersamplesfrom2010fromthewellsshowninFigure 3.3.5 provideanotherthreetransectsdowngradientfromthesourceareas.MassdischargevalueswerecalculatedforboththeEasternandWesternsourceareasusingEquation 2 .TheresultingmassdischargevaluesareshowninTables 3-4 and 3-5 Figure3-1. WellandTransectLocationsatNASJacksonville( CH2MHill 2008 ) 31

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Table3-1. CalculatedMassDischargeatNASJacksonville TransectWelldyTCEEquivalentsMassDischargeErrorm/Lg/day% B-B'MW3727.4400128MW3521.348183460509736MW3824.39292639736.3224.22 C-C'MW4130.491171177213156MW4030.4931323073800365959281939MW4230.490102449.3118.56 32

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Figure3-2. WellandTransectLocationsatEdinburoughSite,Adelaide,Australia( Basuetal. 2009 ) Table3-2. CalculatedMassDischargeatEdinburoughSite,Adelaide,Australia TransectWelldydzTCEFluxMassDischargeErrormmmg/m2/dayg/day% SourceMW113.8311.513.863.313.8815.1MW22.885.32.896.2MW33.880.73.890.1MW45.680.45.690.12.7416.75 PlumeMW24113.9910.2MW21813.986.5MW519.892.919.884.2MW625.691.5MW21925.689.05.3712.2 33

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Figure3-3. WellandTransectLocationatCalfPasturePoint,RhodeIsland( TetraTech 2008 ) 34

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Table3-3. CalculatedMassDischargeatCalfPasturePoint,RhodeIsland DateWellTCEEquivalentsMassDischargeError/Lg/day% May-9604D10600005D8500017D172000308.8928.6 Feb-0704D1500005D1000017D6800089.4434 Nov-0704D1500005D500017D4600020.4435 May-0804D1400005D600017D5100065.1334.85 Oct-0804D1500005D800017D197000229.9537.7 April-0904D1500005D700017D6300079.8335.1 Sept-0904D1100005D500017D5300065.9135.7 April-1004D1100005D500017D4700057.0335.1 Table3-4. CalculatedMassDischargeatHangarKEast TransectYearMassDischargeErrorg/day% East12002290.36116.0East22002572.25512.3East32002406.30711.3East12010114.50111.5East22010128.81818.6East32010277.10915.2 35

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Figure3-4. DPTLocationsatHangarK( COREEngineeringConstruction,Inc. 2009 ) Figure3-5. WellLocationsatHangarK( BEMSystems,Inc. 2002 ) 36

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Table3-5. CalculatedMassDischargeatHangarKWest TransectYearMassDischargeErrorg/day% West12002348.80016.5West22002160.82014.9West32002174.45013.7West12010495.39710.6West22010230.27820.2West32010161.47120.5 37

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CHAPTER4CODEDEVELOPMENTThreepubliclyavailablecodesthatsolvegoverningequationsforgroundwaterowandcontaminanttransportwereoriginallyinvestigatedforachievingtheobjectivesofthisresearch.ThecodesutilizedwereMichiganStateUniversity'sInteractiveGroundwater(IGW),EPA'sRemediationEvaluationModelofChlorinatedSolvents(REMChlor),andUSGS'sModularThree-DimensionalFinite-DifferenceGroundwaterFlowModel(MODFLOW)withEPA'stransportcodeMT3D( Faltaetal. 2007 ; Harbaugh 2005 ; LiandLiu 2004 ; ZhengandWang 1999 ).Afterworkingwiththesemodelingprograms,itsoonbecameevidentthatitwouldnotbepossibletoefcientlyandsystematicallyevaluatearangeofpossiblesourcestrengthfunctionparametercombinationsusinganexistinggroundwatermodelingprogram.TheonlyprogramtohaveabuiltinsourcestrengthfunctionwasREMChlorwhichcontaineduser-speciedPLmodelparameters.EvenwhenusingthePLmodelwithinREMChlortoinvestigatesites,systematicevaluationofpossibleparametervalueswouldrequiresignicanteffort.Eachcombinationofgamma,mass,concentration,timeofrelease,anddispersivitymustbeinputintotheprogram.Aftertheprogramwasrun,thedatahadtobeextractedandexternallycomparedtotheactualconcentrationswithagoodness-of-tparameter,orobjectivefunction.Thisprocesswouldhavetoberepeateduntilallpossibleinputparametercombinationswereexhausted.Ifthelocationofthesourcewasalsoconsideredanunknown,thisprocesswouldbecomeevenmorecomplicatedasthelocationsforthedatatobeextractedwouldhavetobeadjusteddependingonthesourcelocationbeinginvestigated.Ifotherprogramsorsourcestrengthfunctionswereused,anadditionalstepwouldhavetobeintroducedinwhichtheuserimportsatimeseriesofsourceconcentrationswhichwerecalculatedexternallyusingthedesiredsourcestrengthfunctionparameters.Becauseofthedifcultiesposedbyexisting 38

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groundwatermodelingcodes,acodewasdevelopedspecicallyforusingahistoricaldatasettodeterminethebesttSSFparameters. 4.1GeneralCode 4.1.1AlgorithmSelectionAgeneticalgorithmapproachwasoriginallyinvestigatedforinverselymodelingthesourcestrengthparametersattheselectedsiteswhenaglobaltwasbeingperformed.Becauseofthelargerdatasetsassociatedwithaglobaltandthenecessityoflinkingthesourcestrengthfunctionstotheadvectiondispersionmodelwhichcanbetimeconsumingtosolve,itwasmorepracticaltosacricetimeforaccuracy.Thegeneticalgorithmranfasterthananexhaustiveorbrute-forcesearchbecauseitwouldrunforauserspeciednumberofgenerations(here1,000).Intherstgeneration,apopulationofindividuals,onethousand,wouldberandomlygenerated.Eachindividualwouldcontainasetofttingparametercombinations.Thentheindividualsproducingthebesttswouldcombinetoproduceanewsetofonethousandindividualsandsomerandommutationswouldbeintroducedtosomeoftheindividualstoaddtothepossibilityofndingabettersolutionthanthosetestedinthepreviousgeneration.Thisprocesswouldberepeateduntilonethousandgenerationshadtakenplace.Withthegeneticalgorithmthesameanswermaynotbefoundeverytimebecausethenalanswerisbasedonseveralrandomselections,theoriginalrandomindividualsintherstgenerationandtherandommatingandmutations.Itwasdifculttoguaranteethesameoutputwitheveryrunofthegeneticalgorithmandthegeneticalgorithmwaschallengingtoimplementduetoitsmorecomplexmethodofsamplingthepossibleinputparametercombinations.Becauseofthesmallerdatasetsgenerallyassociatedwiththetransectandpumpingwellmethodsandthusshortercomputationtimes,theexhaustivesearchalgorithmwaspursuedforthethreemethodsinvestigatedhere.Theexhaustivesearchissimpletounderstand,simpletoimplement, 39

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andcanlocatethebestsolutioneverytimeitisrunbecausetheoutputisnotafunctionoftheoptimizationroutine. 4.1.2ExhaustiveSearchFrameworkEachexhaustivesearchcodewrittenfortheobjectivesofthispaperhasthefollowingfourcomponents. 1. Readsale-Thecodereadsthelecontainingtheelddataandtheassociatedspatialandtemporalcoordinates.Itthensavesthevaluesinasetofarrays 2. Assignsparametervalues-Ifavariableisassumedtobeknown,theknownvalueisassigned.Ifthevariablewasnotknown,areasonablerangeofvaluesandtheintervalatwhichthatrangeistobeinvestigatedisassignedtothevariableusingado-loop. 3. Equations-Asetofequationsissolvedusingeachsetofpossibleinputsfortheunknownparameters.ThePLandESTmodelswerethetwoSSFusedinthecodespresentedaspartofthisstudy.TheadvectiondispersionequationissolvedusingapublicallyavailableFORTRANsubroutinepackagecalledQUADPACK( Piessensetal. 1983 ).QUADPACKsolvesthedeniteintegralusinganiterativeapproach. 4. ObjectiveFunction-Anobjectivefunctionissolvedforeachsetofpossibleinputs.Theobjectivefunctionisafunctionthatcomparesthecalculatedvaluestothevaluesintheelddataset.Theobjectivefunctionprovidesametricbywhichthebesttsetofparameterscanbedetermined. 4.1.2.1SourcezonepumpingtwithPLmodelToutilizethePLmodelwhenevaluatingthesourcezonepumpingdatafromHillAFB,thePLmodelwasmodiedandwrittenintermsofthecumulativevolumeofwaterthathaspassedthroughthesourcezone.ThiswasdonebyreplacingtheVdAtterminEquations 2 2 ,and 2 withthecumulativewaterpumpedthroughthesourcezoneresultinginEquations 4 4 ,and 4 Cs(t)=Co M)]TJ /F9 7.97 Tf -.93 -6.41 Td[(o()]TJ /F2 11.955 Tf 14.32 0 Td[()]TJ /F3 11.955 Tf 11.95 0 Td[(1)VcCo M)]TJ /F9 7.97 Tf -.93 -6.41 Td[(o+M1)]TJ /F10 7.97 Tf 6.58 0 Td[()]TJ /F9 7.97 Tf -11.95 -7.89 Td[(o)]TJ ET q .359 w 323.32 -554.75 m 336.02 -554.75 l S Q BT /F7 5.978 Tf 323.32 -559.87 Td[(1)]TJ /F7 5.978 Tf 5.75 0 Td[()]TJ /F1 11.955 Tf 107.7 -11.06 Td[((4) Cs(t)=Coe)]TJ /F14 5.978 Tf 5.76 0 Td[(VcCo Mo(4) Cs(t)=Co)]TJ /F5 11.955 Tf 13.15 8.09 Td[(VcC2o 2Mo(4) 40

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Whenusingpumpingdata,itiseasytocalculatethecumulativemassremovedandthusitispossibletodetermineasetofbesttparametersusingcumulativemassremovedinsteadofconcentrationdata.Equations 2 and 2 wererewrittenintermsofVcandsubtractedtofromMotoresultinEquations 4 and 4 whichcumulativemassremoved. M(t)=Mo)]TJ /F11 11.955 Tf 11.96 16.85 Td[(()]TJ /F2 11.955 Tf 14.31 0 Td[()]TJ /F3 11.955 Tf 11.96 0 Td[(1)VcCo M)]TJ /F9 7.97 Tf -.93 -6.41 Td[(o+M1)]TJ /F10 7.97 Tf 6.59 0 Td[()]TJ /F9 7.97 Tf -11.96 -7.89 Td[(o)]TJ ET q .359 w 327.52 -115.32 m 340.22 -115.32 l S Q BT /F7 5.978 Tf 327.52 -120.44 Td[(1)]TJ /F7 5.978 Tf 5.76 0 Td[()]TJ /F1 11.955 Tf 103.5 -11.05 Td[((4) M(t)=Mo)]TJ /F5 11.955 Tf 11.96 0 Td[(Moe)]TJ /F14 5.978 Tf 7.78 3.53 Td[(VcCo Mo(4)TomakethemodelmorecomparabletotheESTmodel,theCotermsinthePLmodelequationswerereplacedwithCsolf.c.whereCsolistheknownsolubilitylimitofthecontaminantinwaterandf.c.isthefractionofthesourcethatiscontaminated.Appendix B containsthecodeusedforHillAFB.Becausethepumpingwellswerewithinthesourcezone,noADEhadtobesolved.Inthisscenario,therearethreettingparameters.Thettingparametersaref.c.,Mo,and)]TJ /F1 11.955 Tf 6.77 0 Td[(. 4.1.2.2PumpingmethodwithESTmodelTheESTModelisformulatedintermsofporevolumesthathavepassedthroughthesourcezone.Tonondimensionalizethecumulativevolumeofwaterpumpedthroughthesourcezone,thevolumehastobedividedbythesourcearea.Thesourceareaisrarelyknownandthusbecomesattingparameter.Appendix B containsthecodeusedforobtainingthebesttparametersfortheESTmodelatHillAFB.Thettingparametersareln,ln,f.c.,andsourcevolume(Vs). 4.1.2.3TransectmethodwithPLandESTmodelWhenestimatingthebestsourcestrengthparametersusingmassdischargedatabasedontransects,theproblemwasapproachedusingaone-dimensionalformofthesourcestrengthfunctionsandcontaminanttransportequation.Theone-dimensionalcodewaschosentocutbackonthenumberofunknowninputparametersaswellasthecomputationtime.Abenetofusingmassdischargevaluesisthatitallowsforthe 41

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three-dimensionalsitestobeeasilyandaccuratelycompressedtoone-dimensionalproblems.Itwasassumed,thattheone-dimensionalcodecanbeappliedtothesethree-dimensionalsitesbecausetheadditionoftransverseandverticaldispersiondoesnotaffectthemassdischargevaluesatapointinthelongitudinaldirection.Whenusingthethree-dimensionalformofthePLequationstheCocanbereplacedwithf.c.usingtherelationshipshowninEquation 4 Co=f.c.Csol(4)NowboththePLandESTmodelscontainthef.c.term.Withthethree-dimensionalESTmodel,thef.c.termrepresentedthepercentageofcontaminatedstreamtubesinthesourcezone.WhenthePLandESTmodelsareone-dimensionalizedthef.c.termnolongerhasthesamephysicalmeaning.Thef.c.valuenowrepresentsthecross-sectionalareaofthecontaminatedfractionofthesourcecross-sectionalareaorthecross-sectionalareathesourcewouldhaveifitwasthree-dimensionalandhadanf.c.ofone.Becauseofthisnewphysicalmeaning,thef.c.termwaschangedtobetheAfterm.Inordertoone-dimensionalizethePLModelasecondchangehadtobemade;thecross-sectionalareatermwasremoved.TheESTModeldidnotcontainacross-sectionalareatermandthusnofurtherchangesweremade.Theone-dimensionalizedversionofthePLmodelequationsareshowninEquations 4 4 ,and 4 .Theone-dimensionalizedversionoftheESTmodelequationisshowninEquation 4 Cs(t)=Af M)]TJ /F9 7.97 Tf -.93 -6.4 Td[(o)]TJ /F5 11.955 Tf 9.3 0 Td[(VdAf sM)]TJ /F9 7.97 Tf -.93 -6.4 Td[(o+M1)]TJ /F10 7.97 Tf 6.58 0 Td[()]TJ /F9 7.97 Tf -11.95 -7.89 Td[(o+VdAf sM)]TJ /F9 7.97 Tf -.93 -6.4 Td[(oe()]TJ /F12 7.97 Tf 8.27 0 Td[()]TJ /F10 7.97 Tf 6.59 0 Td[(1)st)]TJ ET q .359 w 362.61 -510.98 m 375.31 -510.98 l S Q BT /F7 5.978 Tf 362.61 -516.09 Td[(1)]TJ /F7 5.978 Tf 5.75 0 Td[()]TJ /F1 11.955 Tf 68.41 -11.06 Td[((4) Cs(t)=Coe)]TJ /F14 5.978 Tf 5.76 0 Td[(VdAf Mot(4) Cs(t)=Co)]TJ /F5 11.955 Tf 13.15 8.08 Td[(VdA2f 2Mot(4) 42

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r Cf(T)=AfCs(1)]TJ /F5 11.955 Tf 11.96 0 Td[(p())(4)Tomakethecontaminanttransportequationone-dimensional,thefyandfzwereexcludedfromEquation 2 resultinginEquation 4 C(x,y,z,t)=Zt0Cs(t)]TJ /F6 11.955 Tf 11.96 0 Td[()@B(x,) @d(4)Appendix B containsthecodesusedforevaluatingthePLandESTmodels,respectively,atNASJax,SalisburySite,andCalfPasturePoint.ForthePLmodel,therewerethefollowing7parameters:Af,Mo,)]TJ /F1 11.955 Tf 6.77 0 Td[(,vd,,timeofrelease(to),andlocationofrelease(xo).toandxowereusedtoadjustthetimeandspatialcoordinatesofthedataset.Theretardationfactorwassetto1andthettedvelocitywasassumedtocapturetheeffectsofretardation.FortheESTmodel,therewerethefollowing8parameters:ln,ln,Af,sl,vd,,to,andxo. 4.1.2.4ObjectivefunctionsForeachsiteandeachSSF,theexhaustivesearchwasperformedusingthecoefcientofefciency(COE)asanobjectivefunction( NashandSutcliffe 1970 ).Thecoefcientofefciencyisdenedas Ce=Pni=1(Qno)]TJ /F5 11.955 Tf 11.95 0 Td[(Qnm)2 Pni=1(Qno)]TJ /F3 11.955 Tf 16.25 2.66 Td[(Qo)2(4)where,Qoistheobserveddata,Qmisthemodeleddata,andnrepresentsthenumberofdatapointsinthedataset.Thecoefcientofefciencyequationhasarangefromto1with1representingaperfectt.Acoefcientofefciencyof0indicatesthatthemeanofthedataisasaccurateasthemodeleddata.Thecoefcientofefciencywaschosenbecauseitisnotafunctionofthesizeofadatasetortherangeofdatavalues.Additionally,itiseasiertodifferentiatebetweenapoortandagoodttothedata. 43

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4.2CodeValidationThecodewasvalidatedusingsyntheticmassdischargedatasetscreatedusingMODFLOWandMT3D.Todothis,sixscenariosinwhichalltheparameterswereknownweresimulatedinthegraphicaluserinterface,GroundwaterModelingSystems(GMS),andthemassdischargeatcertainpointsalongtheplumewereextractedfromtheconcentrationdatacalculatedbyMT3D.OfthesixscenariosthreeinvestigatethePLModelandthreeinvestigateESTModel.ThesixSSFsimportedintheGMSareshowninFigure 4-1 .MODFLOWandMT3DwerechosenoverIGWandREMchlorbecausetheyweretheeasiesttouseandtheywerethemostwelldocumented.Then,theexhaustivesearchalgorithminAppendix B wasrunwithmassdischargevaluesextractedfromMT3D.Aonelayermodelthatcontains20011x1x1mgridcellswasused.Themodelhadconstantheadboundariesoneachendwhichcorrespondedtoahydraulicgradientof0.1.Thehydraulicconductivitywassetat0.3m/dayandtheporositywasaconstantof0.3leadingtoaDarcyvelocityof0.1m/day.Thedispersivitycoefcientinthelongitudinaldirectionwassetat5meters.Thesourcestrengthfunctionwasimportedintotherstgridcellataresolutionofevery0.05yearsor20timesayearfor40yearsbeginningin1970.Theinitialmasswas500kg.Theinitialconcentrationwas1.1g/LcorrespondingtoaAfof1.0. 4.2.1ValidationwithaSyntheticTemporalDataSetToinvestigatethebehavioroftheexhaustivesearchalgorithmwhenusingtemporalmassdischargedata,theexhaustivesearchalgorithmwasrunsixtimes,forthree)]TJ /F1 11.955 Tf -434.18 -23.91 Td[(valuesandthreelnvalue,with20datapointscorrespondingtoonedatapointeveryyearfromzerototwentyyearssincethespillat40metersdowngradient.ThegurescontainingsynethticdatahaveallbeenplotedusingEquations 4 and 4 whicharedimensionlessparametersproposedbyGuyonnetandNeville( 2004 ). tD=vt Rxo(4) 44

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A=)]TJ /F18 9.963 Tf 8.42 0 Td[(=0.2 B=)]TJ /F18 9.963 Tf 8.42 0 Td[(=1.2 C=)]TJ /F18 9.963 Tf 8.41 0 Td[(=2.0Figure4-1. SyntethicDataSSFs 45

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Table4-1. BestFitPLModelParametersusing20SyntheticTemporalMassDischargeDataPoints Parameter)]TJ /F1 11.955 Tf 10.09 0 Td[(=0.2)]TJ /F1 11.955 Tf 6.77 0 Td[(=1.2)]TJ /F1 11.955 Tf 10.1 0 Td[(=2.0ParameterRange )]TJ /F1 11.955 Tf 45.32 0 Td[(0.21.21.70-2(by0.1)Af0.90.90.90.9,1.0,1.1Mo(kg)500500450450,500,550vd(m/d)0.110.110.110.09,0.1,0.11xo(m)-1-1-1-1,0,1to1970197019701969,1970,1971x(m)5551,5,9Ce0.998900.999380.99948 XD=x xo(4)where,xoisaarbitrarydistanceinthexdirection.ForalltDandXDvaluesinthispaper,xo=1000m.Figure 4-2 presentsthesyntheticdatasetsatadistanceof40metersfromthesource.Tables 4-1 and 4-2 showsthebesttparametersfoundbythealgorithm.TheexhaustivesearchwasrerunforeachofthesixscenariosusingonlythethreedatapointsmarkedbycirclesinFigure 4-2 .Thelocationsofthesethreedatapointswerechoseninanattempttohavethreepointscapturingthemajorityofthedissolutioncurve.TheseresultsareshowninTables 4-3 and 4-4 .ThenalcolumnsofTables 4-1 to 4-4 showthevaluesinvestigatedforeachparameter.Theexhaustivesearchalgorithmwasabletolocatethecorrect)]TJ /F1 11.955 Tf 10.1 0 Td[(andlnforallcasesusing20datapointswiththeexceptionofthe)]TJ /F1 11.955 Tf 10.1 0 Td[(=2.0case.Thealgorithmwasnotassuccessfulatlocatingthecorrectvaluesfortheotherparameters.Whenusingonlythreedatapoints,thealgorithmlocatedthecorrect)]TJ /F1 11.955 Tf 10.1 0 Td[(andlnforeverycase.AllbesttparametercombinationsforthetemporaldatasetsledtoCOEthatroundedto1.00. 4.2.2ValidationwithSpatialDataToinvestigatethebehavioroftheexhaustivesearchalgorithmwhenspatialtransectdatawasbeingused,thealgorithmwasrunwithspatialsyntheticdatasetsatagesof25%,50%,and75%forvarious)]TJ /F1 11.955 Tf 10.1 0 Td[(andlnvaluesandvaryqualitiesofdatasets.Duetotimeconstraintsnotall)]TJ /F1 11.955 Tf 10.1 0 Td[(andlnvalueswereinvestigatedforeachsiteage. 46

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APLModel BESTModelFigure4-2. SyntheticTemporalDataat40Meters Table4-2. BestFitESTModelParametersusing20SyntheticTemporalMassDischargeDataPoints Parameterln=0.2ln=1.2ln=2.0ParameterRange ln0.21.22.00-2(by0.1)ln5.13.92.6varies(10values)Af0.90.90.90.8-1.2(by0.1)sl3.05.05.01-5(by1)vd(m/d)0.110.110.110.08-0.12(by0.01)xo(m)-1-1-1(-2)-(+2)(by1)to1970197019701968-1972(by1)x(m)5551-13(by4)Mo(kg)497502492Ce0.999710.999790.99953 47

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Table4-3. BestFitPLModelParametersusing3SyntheticTemporalMassDischargeDataPoints Parameter)]TJ /F1 11.955 Tf 10.09 0 Td[(=0.2)]TJ /F1 11.955 Tf 10.09 0 Td[(=1.2)]TJ /F1 11.955 Tf 10.1 0 Td[(=2.0ParameterRange )]TJ /F1 11.955 Tf 45.32 0 Td[(0.21.22.00-2(by0.1)Af0.90.91.00.9,1.0,1.1Mo(kg)500500500450,500,550vd(m/d)0.110.110.100.09,0.1,0.11xo(m)-1-1-1-1,0,1to1970197019701969,1970,1971x(m)5511,5,9Ce0.998900.999380.99998 Table4-4. BestFitESTModelParametersusing3SyntheticMassDischargeDataPoints Parameterln=0.2ln=1.2ln=2.0ParameterRange ln0.21.22.00-2(by0.1)ln4.64.73.0varies(10values)Af0.91.01.00.8-1.2(by0.1)sl5231-5(by1)vd(m/d)0.110.100.100.08-0.12(by0.01)xo(m)-2-21(-2)-(+2)(by1)to1970197019701968-1972(by1)x(m)1511-13(by4)Mo(kg)502497490Ce0.999990.999990.99999 4.2.2.1Validationwithasyntheticspatialdatasetatasiteageof25%Tovalidatethespatialtransectcase,thesamemodelwasusedandthedatacollectedwasevenlyspacedspatiallywithintheplumeatthetimewhenthesitehadreachedasiteageof25%forthePLModel.Figure 4-3 presentsthesyntheticdatasetsingraphicalform.Table 4-5 showsthebesttparametersfoundbythealgorithm.TheexhaustivesearchwasrerunforeachofthesixscenariosusingonlythethreedatapointsmarkedbycirclesinFigure 4-3 .TheseresultsareshowninTables 4-6 and 4-6 .ThenalcolumnsofTables 4-5 and 4-6 showthevaluesinvestigatedforeachparameter.Theexhaustivesearchalgorithmwasunabletolocatethecorrectvaluesfor)]TJ /F1 11.955 Tf 10.1 0 Td[(andlnwhenthesiteswereonlyage25%;however,allbesttparametercombinationsresultedinCOEof0.99orgreater. 48

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Figure4-3. SyntheticSpatialDataataSiteAgeof25% Table4-5. BestFitPLModelParametersusing20SyntheticSpatialDataPointsatanAgeof25% Parameter)]TJ /F1 11.955 Tf 10.09 0 Td[(=0.2)]TJ /F1 11.955 Tf 10.09 0 Td[(=1.2)]TJ /F1 11.955 Tf 10.1 0 Td[(=2.0ParameterRange )]TJ /F1 11.955 Tf 45.32 0 Td[(0.01.81.80-2(by0.1)Af1.11.11.10.8-1.2(by0.1)Mo(kg)460540460450-550(by10)vd0.080.110.110.08-0.12(by0.01)xo-1-2-2(-2)-(+2)(by1.0)to1969197019701968-1972(by1.0)x(m)5551-13(by4)Ce0.999090.998370.99201 Table4-6. BestFitPLModelParametersusing3SyntheticSpatialDataPointsatanAgeof25% Parameter)]TJ /F1 11.955 Tf 10.09 0 Td[(=0.2)]TJ /F1 11.955 Tf 10.09 0 Td[(=1.2)]TJ /F1 11.955 Tf 10.1 0 Td[(=2.0ParameterRange )]TJ /F1 11.955 Tf 45.32 0 Td[(0.51.20.80-2(by0.1)Af1.11.20.80.8-1.2(by0.1)Mo(kg)460530470450-550(by10)vd0.100.100.110.08-0.12(by0.01)xo-222(-2)-(+2)(by1.0)to1970197019701968-1972(by1.0)x(m)9911-13(by4)Ce0.999990.998190.99948 49

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Table4-7. BestFitParametersusing20SyntheticSpatialDataPointsatanAgeof50% Parameter)]TJ /F1 11.955 Tf 10.09 0 Td[(=0.2)]TJ /F1 11.955 Tf 10.09 0 Td[(=1.2)]TJ /F1 11.955 Tf 10.1 0 Td[(=2.0ParameterRange )]TJ /F1 11.955 Tf 45.32 0 Td[(0.21.12.00-2(by0.1)Af1.01.00.90.8-1.2(by0.1)Mo(kg)510470460450-550(by10)vd0.100.100.110.08-0.12(by0.01)xo-2-20(-2)-(+2)(by1.0)to1970197019711968-1972(by1.0)x(m)5551-13(by4)Ce0.999340.990910.99968 4.2.2.2Validationwithasyntheticspatialdatasetatasiteageof50%Thesamemodelwasusedandthedatacollectedwasevenlyspacedspatiallywithintheplumeatthetimewhenthesitehadreachedasiteageof50%.Figure 4-4 presentsthesyntheticdatasets.Tables 4-7 and 4-8 showsthebesttparametersfoundbythealgorithm.TheexhaustivesearchwasalsorunforeachofthesixscenariosusingonlythethreedatapointsmarkedbycirclesinFigure 4-4 .TheseresultsareshowninTables 4-9 nad 4-10 .ThenalcolumnsofTables 4-7 to 4-10 showthevaluesinvestigatedforeachparameter.Atasiteageof50%thealgorithmsperformedmuchbetterthanatasiteageof25%.ForboththePLandESTmodels,theexhaustivesearchalgorithmwasabletocomewithintwotenthsofthecorrect)]TJ /F1 11.955 Tf 10.1 0 Td[(andlnvalueswhenusingdatasetsoftwenty.Whenusingonlythreedatapoints,thealgorithmlocatedthecorrect)]TJ /F1 11.955 Tf 10.09 0 Td[(andlnwithinthreetenthsforallthecasesexcept)]TJ /F1 11.955 Tf 10.09 0 Td[(equals2.0.AllcombinationsofbesttsparametersgaveCOEthatroundedto1.00. 4.2.2.3Validationwithasyntheticspatialdatasetatasiteageof75%ThePLModelwastheninvestigatedatasiteageof75%usingthedatashowninFigure 4-5 .Table 4-11 showsthebesttparametersfoundbytheexhaustivesearchalgorithm.Table 4-12 showstheresultingbesttparameterswhentheexhaustivesearchwasrunusingonlythethreepointsrespresentedwithcirclesinFigure 4-5 .Whenthesiteagewas75%thesitebehavedsimilarlytothecaseswhenthesiteswere50% 50

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Table4-8. BestFitESTModelParametersusing20SyntheticSpatialDataPointsatanAgeof50% Parameterln=0.2ln=1.2ln=2.0ParameterRange ln0.01.41.90-2(by0.1)ln5.14.12.9varies(10values)Af1.01.10.90.8-1.2(by0.1)sl4.03.04.01-5(by1)vd(m/d)0.100.100.110.08-0.12(by0.01)xo(m)-2-1-1(-2)-(+2)(by1)to1970197019721968-1972(by1)x(m)5551-13(by4)Mo(kg)721584437Ce0.999420.9997120.99997 Table4-9. BestFitPLModelParametersusing3SyntheticSpatialDataPointsatanAgeof50% Parameter)]TJ /F1 11.955 Tf 10.09 0 Td[(=0.2)]TJ /F1 11.955 Tf 10.09 0 Td[(=1.2)]TJ /F1 11.955 Tf 10.1 0 Td[(=2.0ParameterRange )]TJ /F1 11.955 Tf 45.32 0 Td[(0.51.20.80-2(by0.1)Af1.11.20.80.8-1.2(by0.1)Mo(kg)460530470450-550(by10)vd0.100.100.110.08-0.12(by0.01)xo-222(-2)-(+2)(by1.0)to1970197019701968-1972(by1.0)x(m)9911-13(by4)Ce0.999990.998190.99948 Table4-10. BestFitESTModelParametersusing3SyntheticSpatialDataPointsatanAgeof50% Parameterln=0.2ln=1.2ln=2.0ParameterRange ln0.41.21.90-2(by0.1)ln5.54.62.9varies(10values)Af1.21.00.90.8-1.2(by0.1)sl1.02.04.01-5(by1)vd(m/d)0.100.120.110.08-0.12(by0.01)xo(m)-2-10(-2)-(+2)(by1)to1971197119721968-1972(by1)x(m)9151-13(by4)Mo(kg)350450438Ce1.000000.999990.99998 51

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APLModel BESTModelFigure4-4. SyntheticSpatialDataataSiteAgeof50% aged.Again,thealgorithmlocatedthecorrect)]TJ /F1 11.955 Tf 10.1 0 Td[(andlnwithintwotenthsforallcasesexceptwhen)]TJ /F1 11.955 Tf 10.1 0 Td[(equals2.0. 4.2.3InvestigationintotheImportanceofSpatialResolutionoftheDataTodeterminewhethersmallchangesinthedataresolutionhadaneffectonthebesttparametersfoundbythealgorithm,thecaseofgammaof0.2wasruntwomoretimes.Firstthemodelwasrunandthespatialdatawasreportedeveryvemeters 52

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Figure4-5. SyntheticSpatialDataataSiteAgeof75% Table4-11. BestFitParametersusing20SyntheticSpatialDataPointsatanAgeof75% Parameter)]TJ /F1 11.955 Tf 10.09 0 Td[(=0.2)]TJ /F1 11.955 Tf 10.09 0 Td[(=1.2ParameterRange )]TJ /F1 11.955 Tf 45.32 0 Td[(0.21.40-2(by0.1)Af1.01.00.8-1.2(by0.1)Mo(kg)500470450-550(by10)vd0.100.100.08-0.12(by0.01)xo-2-2(-2)-(+2)(by1.0)to197019701968-1972(by1.0)x(m)551-13(by4)Ce0.999320.99091 Table4-12. BestFitParametersusing3SyntheticSpatialDataPointsatanAgeof75% Parameter)]TJ /F1 11.955 Tf 10.09 0 Td[(=0.2)]TJ /F1 11.955 Tf 10.09 0 Td[(=1.2)]TJ /F1 11.955 Tf 10.1 0 Td[(=2.0ParameterRange )]TJ /F1 11.955 Tf 45.32 0 Td[(0.21.11.40-2(by0.1)Af1.01.01.20.8-1.2(by0.1)Mo(kg)500480470450-550(by10)vd0.100.100.100.08-0.12(by0.01)xo-2-1-1(-2)-(+2)(by1.0)to1970197019721968-1972(by1.0)x(m)5591-13(by4)Ce0.999980.999941.00000 53

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Table4-13. BestFitParametersusingVariousDataResolutionwitha)]TJ /F1 11.955 Tf 10.1 0 Td[(of0.2atanAgeof25% ParameterEvery5metersEvery10metersEvery20metersParameterRange )]TJ /F1 11.955 Tf 82.56 0 Td[(0.00.00.00-2(by0.1)Af1.21.21.20.8-1.2(by0.1)Mo(kg)470460480450-550(by10)vd0.080.080.080.08-0.12(by0.01)xo-1-1-1(-2)-(+2)(by1.0)to1969196919691968-1972(by1.0)x(m)5551-13(by4)Ce0.999020.999090.99905 Table4-14. BestFitPLModelParametersusingCombinationsof3SyntheticSpatialDataPoints ParameterCase1Case2Case3ParameterRange )]TJ /F1 11.955 Tf 45.32 0 Td[(1.20.42.00-2(by0.1)Af1.01.01.10.8-1.2(by0.1)Mo(kg)510500550450-550(by10)vd0.090.080.100.08-0.12(by0.01)xo22-2(-2)-(+2)(by1.0)to1970196819701968-1972(by1.0)x(m)5151-13(by4)Ce0.999990.9997450.99999 downgradientwhichresultedin40pointsinthedataset.Next,themodelwasrunandthespatialdatawasreportedevery20meterswhichresultedinadatasetcomprisedof10points.ThebesttparametersforallthreecasesareshowninTable 4-13 .Thedataresolutionslightlyaffectedthebesttvaluesforinitialmass.Allotherbesttparametersremainedthesameregardlessofthespatialresolution. 4.2.4InvestigationintotheImportanceofLocationofLimitedDataSetsTodeterminetheimportanceoflocationofthedataalongthedissolutionprocesswhenusinglimiteddata,themodelwasrunthreetimesusingdifferentsetsofthreedatapointsforthePLmodelatasiteageof50%witha)]TJ /F1 11.955 Tf 10.1 0 Td[(of1.2.ThedataforthethreecasesisshowninFigure 4-6 .ThebesttparameterresultsareshowninTable 4-14 .Theprocesswasrepeatedusingfourcombinationof2datapoints.ThedataforthefourcasesisshowninFigure 4-7 andthebesttparameterresultsareshowninTable 4-15 54

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Figure4-6. CombinationsofThreeDataPointsfromPLModel Figure4-7. CombinationsofTwoDataPointsfromPLModel 4.3DifferencesbetweenMT3DSolutionsandAnalyticalSolutionsFigure 4-8 illustratestheslightdifferencebetweentheMT3DsolutionandthesolutionformtheFORTRANcodeforthespatialcaseatage50%and)]TJ /F1 11.955 Tf 10.1 0 Td[(equals1.2.ThedifferencebetweenthetwosolutionscouldbeduetothedifferencesintheequationsbythenitedifferencecodeandtheanalyticalequationsusedbytheFORTRANcode.Itisthisdifferencethatcausesmanyofthebesttparamtersfromtheexhaustivesearch 55

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Table4-15. BestFitPLModelParametersusingCombinationsof2SyntheticSpatialDataPoints ParameterCase1Case2Case3Case4 )]TJ /F1 11.955 Tf 45.32 0 Td[(1.21.40.71.40-2(by0.1)Af1.21.11.11.10.8-1.2(by0.1)Mo(kg)460530450530450-550(by10)vd0.100.100.090.100.08-0.12(by0.01)xo-1-22-2(-2)-(+2)(by1.0)to19681970197219701968-1972(by1.0)x(m)15551-13(by4)Ce1.000001.000001.000001.00000 algorithmtobeslightlyofffromthoseinputintoMT3D.Figure 4-9 showsthecorrect Figure4-8. ComparisonbetweentheMT3Dandanalyticalsolutions solutionandbesttsolutionsascalculatedbytheanalyticalsolutionforthecaseoflnis1.2.Thebesttparametersareshownin 4-8 .TheCOEbetweentheMT3Ddataandthecorrectanalyticalsolutionis0.996.TheCOEbetweentheMT3Ddataandthebesttparametersis0.999.ThereasonasetofdifferentparameterswasfoundtobethebesttusingtheexhaustivesearchisduetothedifferencebetweentheMT3Dsolutionsandtheanalyticalsolution. 56

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Figure4-9. AnalyticalsolutionsusingtheBestFitandCorrectPLModelParameters 57

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CHAPTER5RESULTSANDDISCUSSION 5.1HillAFB 5.1.1FittoConcentrationTimeSeriesTheexhaustivesearchalgorithmdescribedinSections4.1.2.1and4.1.2.2wasrunusingtheconcentrationtimeseriesfromthepumpingactivitiesatHillAFB.ThecodeforthisalgorithmcanbefoundinAppendix B .ThecodewasruntwiceusingboththePLandESTmodel.Table 5-1 showsthebesttparametersforeachrun.Figure 5-1 showtimeseriesplotsofthebesttscenarioscomparedtotheconcentrationdataandthecumulativemassremoved.Theresultsindicatelow)]TJ /F1 11.955 Tf 10.09 0 Td[(andlnwhichbothrepresentanearconstantmassdischargefromthesource.TheCOEforthebesttparameterswaslowwhenttingtotheconcentrationtimeseries.Thepoortisduetothemultipleabruptincreasesintheconcentrationvaluesthroughtime. 5.1.2FittoCumulativeMassRemovedDataBecausethecumulativemassremovedcurvesaresmoother,thecodewasrunagainthistimettingtothecumulativemassremovedvalues.TheresultsareshowninTable 5-2 .TheplotsoftheconcentrationtimesseriesandthecumulativemassremovedareshowninFigure 5-2 .Again,theresultsindicatedaconstantmassdischargebutwhenttingtothecumulativemassremoveddatasettheCOEindicatedamuchbettert.Thebettertswereduetothesmoothnessofthecumulativemassremoveddataset. Table5-1. OptimizedSSFParametersatHillAFBusingConcentrationData SSFESTModelPLModel ln1.02N/Aln0.1N/A)]TJ /F1 11.955 Tf 104.57 0 Td[(N/A0.0Af0.210.22Mo(kg)75026910SourceArea(m2)11,740N/ACOE0.250.22 58

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ACoefcientofEfciencyOptimizations-ConcentrationTimeSeries BCoefcientofEfciencyOptimizations-CumulativeMassRemovedFigure5-1. HillAFBConcentrationFitsWithPumpingDatafrom1999-2009 59

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ACoefcientofEfciencyOptimizations-ConcentrationTimeSeries BCoefcientofEfciencyOptimizations-CumulativeMassRemovedFigure5-2. HillAFBFitwithCumulativeMassRemovedDatafromPumpingActivitiesbetween1999-2009 60

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Table5-2. OptimizedSSFParametersusingCumulativeMassRemovedData SSFESTModelPLModel ln1.5N/Aln0.05N/A)]TJ /F1 11.955 Tf 104.57 0 Td[(N/A0.0Af0.160.16Mo(kg)60956041SourceArea(m2)7,760N/ACOE0.990.99 Table5-3. OptimizedSSFParametersusingCumulativeMassRemovedDatawithaSetSourceVolume SSFESTModel ln2.9ln0.12Af0.16COE0.99 5.1.3FittoCumulativeMassRemovedDatawithRestrictedSourceVolumeAsstatedinSection3.3.1,mostoftheDNAPLmassisknowntobeinapaleochannelatthesite.Theareaofthepaleochannelwasestimatedtobe7,000m3.Assumingaporosityof0.3,theporespaceassociatedwiththepaleochannelwouldbeapproximately2,000m3.Inordertolimitthettingparametersandmakethesourceareavaluemorerealistic,thecodewasrunagainsettingthesourcevolumetermintheESTmodelto2,000m3.ThePLModeldoesnotcontainasourcevolumetermsothistwasonlyperformedwiththeESTmodel.TheSSFbesttparametervaluesareshowninTable 5-3 andtheirassociatedplotsareshowninFigure 5-3 5.1.4FittoTruncatedCumulativeMassRemovedDataInFigures 5-1 and 5-2 ,itcanbeseenthatthelatterportionofthedataexhibitsexponentialdecay.Thedataoccuringafterthetimewhen25,000cubicmetershadbeenpumpedthroughthesourcewastusingthecodeinAppendix B toseeifabettertcouldbeproduced.Thedatasetincluded59datapoints.Table 5-4 showstheresultingoptimizedSSFparameters.Figure 5-4 showstheconcentrationandcumulativemassremovedplotscomparedtothedata. 61

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ACoefcientofEfciencyOptimizations-CumulativeMassRemoved BCoefcientofEfciencyOptimizations-ConcentrationTimeSeriesFigure5-3. HillAFBCumulativeMassRemovedFitwithPumpingDatafrom1999-2009andRestrictedSourceVolume 62

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ACoefcientofEfciencyOptimizations-ConcentrationTimeSeries BCoefcientofEfciencyOptimizations-CumulativeMassRemovedFigure5-4. HillAFBFitwithCumulativeMassRemovedDatafromPumpingActivitiesbetween2004to2010 63

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Table5-4. OptimizedSSFParametersusingTruncatedCumulativeMassRemovedData SSFESTModelPLModel ln5.9N/Aln1.7N/A)]TJ /F1 11.955 Tf 104.57 0 Td[(N/A23.0Af0.580.53Mo(kg)2,57014,970SourceArea(m2)2.7N/ACOE1.000.99 5.1.5SensitivityFigure 5-5 showssomeofthebesttstothecumulativemassremovedfomarangeof)]TJ /F1 11.955 Tf 10.1 0 Td[(values.Itcanbeseenthat)]TJ /F1 11.955 Tf 10.1 0 Td[(valuesform0.0to2.0canresultinaCOEabove0.95iftheothertwottingparametersareunrestricted.Inanattempttonarrowtherangeof)]TJ /F1 11.955 Tf 10.1 0 Td[(valuesresultinginCOEabove0.95,theinitialmasspresentinthesourceareaatthebeginningofpumpingwasrestrictedtovaluesbetween6,000and8,000kg.Thesevalueswerebasedonpreviousassessmentsofthemassremaininginthesourcezone.Whenthisrestrictionwasimplement,)]TJ /F1 11.955 Tf 10.09 0 Td[(valuesbetween0.0and0.9werefoundtogiveCOEabove0.95.Theresultingbesttparametercombinationsandtheirassociatedyearsofpumpingtoreach1.0mg/Land5g/LareshowninTable 5-5 .Thetimestoreach1.0mg/L,5g/Land1g/daywerecalculatedusingtheaveragemonthlypumpingratebetween1999and2009whichwas325m3/month.Thevalueof5g/Lwaschosenbecausethisisthemaximumconcentrationlevel(MCL)forTCEsetbytheUnitedStatesEnvironmentalProtectionAgency( EPA 2011 ). 5.2NASJacksonvilleThebesttparametersresultingfromtheexhaustivesearchusingthemassdischargedatafromNASJacksonvilleareshowninTable 5-6 .Tenvalueswereinvestigatedforeachttingparameterresultingin10,000,000combinationsforthePLmodelwheresevenparameterswereconsideredttingparametersand100,000,000combinationsfortheESTmodelwhereeightparameterswerebeingt.Thebesttmodeledmassdischargevaluesareplottedalongwiththemeasuredmassdischarge 64

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Figure5-5. PossiblePLModelFitsatHillAFB Table5-5. AdditionalYearsofPumpingtoreachMCLwithPLModeltswithCOEabove0.95 )]TJ /F1 11.955 Tf 29.02 0 Td[(AfMoCOEV1mg=Lt1mg=LV5g=Lt5g=LV1g=dayt1g=daykgm3yearsm3yearsm3years 0.00.1860400.9925291800291800291800.00.10.1960900.9893323770323770323770.00.20.1980000.9863478472.27478472.27478472.270.30.2080000.9850519483.32519493.32519493.320.40.2180000.9820577044.80577214.80577204.800.50.2280000.9779661156.95661156.95660896.950.60.2380000.9727777069.937899410.237862610.160.70.2480000.96679175213.5310005515.569755915.010.80.2580000.959910973618.1413595729.8612536922.150.90.2680000.952413051223.4719690340.4916419432.10 valuesinFigure 5-6 .Bothmodelstthedatawell.ThePLModelpredictsmuchgreateruxesandtotalmassthantheESTmodel.Ifavailable,additionalsiteinformationsuchasaisoconcentrationmapoftheplumeorknowledgeofhowmuchTCEwasoriginallyreleasedcouldbeusedtodeterminewhichtismorepractical.ItshouldbenotedthattheESTModelwasnotexplicitlygivenarangeofpossiblemassvalues;therefore,the 65

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Table5-6. OptimizedSSFParametersusingNASJacksonvilleData SSFESTModelPLModel ln3.6N/Aln0.8N/A)]TJ /F1 11.955 Tf 110.95 0 Td[(N/A2.0Af3.541Mo(kg)21346000SourceLength(m)11N/Ax(m)15060vd(m/d)0.060.11xo(m)60180to19501960COE1.001.00t1g=day(years)99180t5g=L(years)7289897 100,000,000parametercombinationscouldhaveresultedinarangeofmassvalueslessthanthoseinvestigatedusingthePLmodel. 5.3EdinburoughSiteThebesttparametersresultingfromtheexhaustivesearchusingthemassdischargedatafromEdinburoughareshowninTable 5-7 .Tenvalueswereinvestigatedforeachttingparameterresultingin10,000,000combinationsforthePLmodelwheresevenparameterswereconsideredttingparametersand100,000,000combinationsfortheESTmodelwhereeightparameterswerebeingt.ThemodeledmassdischargevaluesareplottedalongwiththemeasuredmassdischargevaluesinFigure 5-7 .AgainbothmodelstthedatawellwiththePLModelpredictingagreatertotalmass. 5.4CalfPasturePointThebesttparametersresultingfromtheexhaustivesearchusingthemassdischargedatafromCalfPasturePointareshowninTable 5-8 .Tenvalueswereinvestigatedforeachttingparameterresultingin10,000,000combinationsforthePLmodelwheresevenparameterswereconsideredttingparametersand100,000,000combinationsfortheESTmodelwhereeightparameterswerebeingt.Themodeled 66

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AESTModel BPLModelFigure5-6. ModeledMassDischargeatNASJacksonvillein2002UsingExhaustiveSearchResults 67

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AESTModel BPLModelFigure5-7. ModeledMassDischargeatEdinburoughin2006UsingExhaustiveSearchResults 68

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Table5-7. OptimizedSSFParametersusingEdinburoughData SSFESTModelPLModel ln1.1N/Aln0.6N/A)]TJ /F1 11.955 Tf 110.95 0 Td[(N/A1.2Af0.50.45Mo(kg)1401000SourceLength(m)71N/Ax(m)150110vd(m/d)0.090.09xo(m)15050to19801955COE1.001.00t1g=day(years)00t5g=L(years)53218 Table5-8. OptimizedSSFParametersusingCalfPasturePointData SSFESTModelPLModel ln1.6N/Aln0.8N/A)]TJ /F1 11.955 Tf 110.95 0 Td[(N/A0.4Af4.5N/AMo(kg)239716000SourceLength(m)71N/Ax(m)70130vd(m/d)0.140.07xo(m)-30-30to19871945COE0.990.99t1g=day(years)51491t5g=L(years)284491 massdischargevaluesareplottedalongwiththemeasuredmassdischargevaluesinFigure 5-8 5.5HangarKEastThebesttparametersresultingfromtheexhaustivesearchusingthemassdischargedatafromHangarKEastareshowninTable 5-9 .Tenvalueswereinvestigatedforeachttingparameterresultingin10,000,000combinationsforthePLmodelwheresevenparameterswereconsideredttingparametersand100,000,000combinations 69

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AESTModelat30MetersDowngradient BPLModelat30MetersDowngradientFigure5-8. ModeledMassDischargeatCalfPasturePointUsingExhaustiveSearchResults 70

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Table5-9. OptimizedSSFParametersusingHangarKEastData SSFESTModelPLModel ln2.6N/Aln0.2N/A)]TJ /F1 11.955 Tf 110.95 0 Td[(N/A0.2Af545Mo(kg)46086000SourceLength(m)61N/Ax(m)6060vd(m/d)0.090.02xo(m)100to19801980COE0.700.82t1g=day(years)140t5g=L(years)340 fortheESTmodelwhereeightparameterswerebeingt.ThemodeledmassdischargevaluesareplottedalongwiththemeasuredmassdischargevaluesinFigure 5-9 .NeithermodeltthedatafromHangarKEastverywell.Bothmodelsseemedunabletotthesharpchangesinobservedspatialmassdischargevalues. 5.6HangarKWestThebesttparametersresultingfromtheexhaustivesearchusingthemassdischargedatafromHangarKWestareshowninTable 5-10 .Tenvalueswereinvestigatedforeachttingparameterresultingin10,000,000combinationsforthePLmodelwheresevenparameterswereconsideredttingparametersand100,000,000combinationsfortheESTmodelwhereeightparameterswerebeingt.ThemodeledmassdischargevaluesareplottedalongwiththemeasuredmassdischargevaluesinFigure 5-10 .NeithermodeltthedatafromHangarKWestverywellasindicatedbythelowCOEvalues.Themodelscouldnottthesuddenspatialdropinmassdischargefoundinthedatawithreasonablelimitsontheparameters.Forexample,thelocationofthesourceisknowntobearoundthersttransectwhichthePLandESTmodelcouldnotjustifyunlessthespilloccurredaftertheuseofTCEwasdiscountinued.Evenwhentheseparameterrestrainswererelaxedthetwaspoor. 71

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AESTModelin2002 BESTModelin2010 CPLModelin2002 DPLModelin2010Figure5-9. ModeledMassDischargeatHangarKEastUsingExhaustiveSearchResults Table5-10. OptimizedSSFParametersusingHangarKWestData SSFESTModelPLModel ln4.6N/Aln0.2N/A)]TJ /F1 11.955 Tf 110.95 0 Td[(N/A2.0Af510Mo(kg)1172365000SourceLength(m)21N/Ax(m)110110vd(m/d)0.060.05xo(m)90230to19901990COE0.190.28t1g=day(years)4277579t5g=L(years)711490713 72

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AESTModelin2002 BESTModelin2010 CPLModelin2002 DPLModelin2010Figure5-10. ModeledMassDischargeatHangarKWestUsingExhaustiveSearchResults 5.7SimLabInordertoassesswhichparametersthetswithelddataweremostsensitiveto,theprogramSimLabwasusedtoperformaMorrissensitivityanalysisforthePLandESTModelatCalfPasturePoint( EuropeanUnion 2008 ).CalfPasturePointwaschosenbecauseitwasthetransectsitewiththelargestdataset.InaMorrissensitivityanalysis,MisanindexofsensitivityoftheoutputtoaparticularparameterandMisanindexofinteractionsbetweentheparameterofinterestandtheotherparameters( Morris 1991 ).TheanalysiswasperformedthreetimesforeachSSFinordertoinvestigatethreedifferentoutputs.Therstoutputwasthecoefcientofefciency.ThiswascalculatedusingthedatasetfromCalfPasturePoint.Thesecondoutputwasthetimeittooktoreachauxof1g/dayandthethirdoutputinvestigatedwasthetimeittooktoreachaconcentrationof5g/L.Thetimeto1g/dayandthetimeto5g/Ldid 73

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notinvolvethecalculationofCOEandthusdidnotinvolveanysitedata.Figures 5-11 and 5-12 showtheresultsoftheSimLabanalysis.ForthePLModel,SimLabfoundtheCOEandtimeto1g/daytobemostsensitivetothevaluesofMoand)]TJ /F1 11.955 Tf 6.77 0 Td[(.Thetimeto5g/Lwasalsoaffectbythesevaluesbutwasmostaffectedbythevalueof)]TJ /F1 11.955 Tf 6.78 0 Td[(.Thisisduetothefactthatthe)]TJ /F1 11.955 Tf 10.09 0 Td[(controlstheamountoftailinganditiswithinthislatterportionofthefunctionthatavalueof5g/Lwouldbeachieved.FortheESTModel,theCOEandtimeto5g/Lwasmostaffectedbythevaluesoflnandsourcelength.Thetimeto1g/daywasmostaffectedbylnandln.ThereasonCOEisnotmoresensitivetolnisuncertain.ItcouldbeanartifactoftheinputdistributionsintoSimLab.Forinstance,arangefrom0.0to2.0wasinvestigatedfor)]TJ /F1 11.955 Tf 10.09 0 Td[(butarangefrom1,000to100,000kgwasinvestigatedforthevalueofMo;botharereasonablerangesforthegivenparameters,butthedisparitybetweenthemagnitudeoftherangesmaycausethesensitivityanalysistooverinterprettheeffectsofMo. 5.8LimitingtheNumberofFittingParametersInanefforttoreducethenumberofpossiblets,EdinburoughandHangarKWestwerebothrunwithfewerttingparameters.TheSimLabresultsindicatethatthevalueofthedispersivitycoefcenthasminimalaffectsonCOE,timeto5g/L,andtimeto1g/daycomparedtotheotherttingparameters.Forthisreason,dispersivitywassetatthebesttvaluesforthesites.Usinginformationaboutthesite,to,xo,andvDwerealsoxed.ThisresultedinthefollowingvettingparametersfortheESTModel:ln,ln,Af,Mo,andsl.ForthePLModel,thettingparameterswerenowMo,Af,and)]TJ /F1 11.955 Tf 6.77 0 Td[(. 5.8.0.1EdinburoughSiteThebesttparametersresultingfromtheexhaustivesearchusingthemassdischargedatafromEdinburoughareshowninthetopportionofTable 5-11 whilethebottomportioncontainsthexedparameters.ThemodeledmassdischargevaluesareplottedalongwiththemeasuredmassdischargevaluesinFigure 5-13 .Bothmodelstthedatawellwithadecreasednumberofttingparameters. 74

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AMorrisSensitivityAnalysisforCOEusingCPPData BMorrisSensitivityAnalysisforTimeto1g/day CMorrisSensitivityAnalysisforTimeto5g/LFigure5-11. MorrisSensitivityAnalysesforthePLModel 75

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AMorrisSensitivityAnalysisforCOEusingCPPData BMorrisSensitivityAnalysisforTimeto1g/day CMorrisSensitivityAnalysisforTimeto5g/LFigure5-12. MorrisSensitivityAnalysesfortheESTModel 76

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AESTModel BPLModelFigure5-13. ModeledMassDischargeatEdinburoughin2006withThreeFixedParameters 77

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Table5-11. OptimizedSSFParametersusingEdinburoughDatawhenThreeParametersareFixed SSFESTModelPLModel ln0.08N/Aln1.1N/A)]TJ /F1 11.955 Tf 110.95 0 Td[(N/A1.5Af1.01.21Mo(kg)109150vd(m/d)0.050.08SourceLength(m)50N/A x(m)110110xo(m)00to19801980COE1.001.00t1g=day(years)130t5g=L(years)250483 5.8.0.2HangarKWestThebesttparametersresultingfromtheexhaustivesearchusingthemassdischargedatafromHangarKWestareshowninthetopportionofTable 5-12 whilethebottomportioncontainsthexedparameters.ThemodeledmassdischargevaluesareplottedalongwiththemeasuredmassdischargevaluesinFigure 5-14 .TheexhaustivesearchwasrstrunwithlessttingparametersandlowervaluesformasswiththePLModeltoseeifthemodelcouldtthedatabetteriflowermasseswereevaluatedbutthebesttresultshittheupperlimitfortheMorange.Withthevaluesforthexedparameters,thebesttparametersindicatedevenhigherMovalues.Bothmodelsfoundbettertswithinthenewparametercombinationsthatwereevaluated.Becauseofthenatureofthedata,neithermodelseemstotthedatawellwithparametersthatseemreasonable.AlthoughthePLModelhasabettert,itpredictsanunreasonablylargemassatthesite. 78

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Table5-12. OptimizedSSFParametersusingHangarKWestDatawhenThreeParametersareFixed SSFESTModelPLModel ln4.8N/Aln0.1N/A)]TJ /F1 11.955 Tf 110.95 0 Td[(N/A0.1Af41450Mo(kg)11,015100,000,000vd(m/d)0.010.09SourceLength(m)2N/A x(m)110110xo(m)00to19801980COE0.420.69t1g=day(years)5835730t5g=L(years)8135730 APLModelin2002 BPLModelin2010 CESTModelin2002 DESTModelin2010Figure5-14. ModeledMassDischargeatHangarKWestwithThreeFixedParameters 79

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CHAPTER6SUMMARYANDFUTURERESEARCHTheprotocolsproposedforestimatingsourcestrengthfunctionsatDNAPLcontaminatedeldsitesincludeanexhaustivesearchalgorithmlinkedtoone-dimensionalsourcestrengthfunctionsandanadvection-dispersionequation.Thealgorithmwassuccessfullyvalidatedusingsyntheticdatasetsthatcapturedthemajorityofthedissolutionprocessatcontaminatedsites.Whenusingthesyntheticdataset,thealgorithmwasabletosuccessfullylocatethecorrectbesttvaluesfortheparametersofinterest,)]TJ /F1 11.955 Tf 10.1 0 Td[(orlnandln,whenthesitewasover50%agedandthetemporalorspatialdatasetcapturedtheentiredisolutionprocess.Theotherparameterswereoftennotcorrectlyoptimizedbythealgorithm,particularly,vD,xo,andto.Theanalysisperformedusingasitethatwas25%agedindicatesthatnotenoughdissolutionhasoccurredtoaccuratelymeasurethesourcestrengthfunctionparameters.Whenusingonlytwoorthreedatapointsfromthesyntheticdataset,thealgorithmwasnotalwayssuccessfulatlocatingthecorrectvaluesforthettingparameters.Withlimiteddata,itappearsthatthealgorithmperformsbestwhenthedatacapturesasignicantmassuxreduction.Whenusinglimitedspatialdata,thismeansthatthebestdatawouldbelocatednearthesource.Whenusinglimitedtemporaldata,thismeansthatthebestdatawouldbethedatacollectedmostrecentlywhenthesiteshaveagedsubstantially.Furtherresearchcouldbeconductedwithsyntheticdatasetstodeterminetheexactmassreductionthatmustbecapturedinsmalldatasetstosuccessfullyimplementtheexhaustivesearchalgorithm.Amajorityoftheeldsitesinvestigateddidnothaveadatasetconducivetousingthepumpingwellorspatialortemporaltransectmethods.Thosesitesthatdidhaveappropriatedataavailableusuallydidnothavealargedataset.AnexceptiontothisisdatasetfromthesourcezonepumpingatHillAFBwhichhad119datapoints.WhenapplyingthepumpingwelltandthetemporaltransectmethodsatHillAFBandCalf 80

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PasturePoint,respectively,tsof0.99werefoundforbothmodels.Whenapplyingthespatialtransectmethodstotheeldsites,goodtswereobtainedattwoofthefourplumes.TheplumesatHangarKwereunabletobettoeithermodelverywelldotothesuddenincreaseinconcentrationsoclosetothesource.TheplumesevaluatedatHangarKweretheonlysystemstoresultinbesttsbelowaCOEof0.9.Despitethesuccessfulvalidationandapplicationoftheproposedprotocols,thebesttparametervaluesfoundusingtheprotocolsareassociatedwithahighlevelofuncertainty.TheuncertaintyispartiallyduetothefactthatthemodelsarehighlysensitivetoseveralofthemodelparameterssoseveralvaluesfortheparametersofinterestcanproducetsaboveaCOEof0.9.Theuncertaintyisalsoafunctionofseveralassumptionsmadewhendevelopingtheprotocols.Thefollowingassumptionsweremade:whenusingmassdischargedatathesitescanbecollapsedtoaone-dimensionalsystem,theheterogeneousoweldsatthesitescanberepresentedbyoneeffectiveDarcyvelocityanddispersivitycoefcient,retardationandDarcyvelocitycanbecollapsedintoonettingparameter,andmassdischargevaluesareunaffectedbythedimensionalityoftheequations.Thecoarsenessoftheintervalsatwhichtheparameterswereinvestigatedandthelackofdatainspaceandtimealsocontributestouncertainty.EvenfortheuniquecaseofHillAFBwhichhadthehighestqualitydatasetandonlythreeparameterswerebeingt,)]TJ /F1 11.955 Tf 10.1 0 Td[(valuesof0.0to0.9producedCOEabove0.95whentheMoterminrestrictedbasedonpreviousestimates.Thesevaluespredictedarangeof0to23.5additionalyearsofpumpinguntilauxof1g/daywouldbereachedand0to40.5additionalyearsofpumpinguntilMCLwouldbereached.Thisrangewouldbelargerifnaturalgradientowwascausingthedissolutioninsteadofpumpingactivities.Attheotherfoursites,theuncertaintyassociatedwiththebesttparametersispredictedtobeevengreaterduetothelargernumberofttingparametersandsmallerdatasets.TheSimLabresultsindicatethatforthePLmodel)]TJ /F1 11.955 Tf 10.1 0 Td[(andMohavethegreatesteffectonCOE,timeto1g/day,andtimetoMCL.Because)]TJ /F1 11.955 Tf 10.1 0 Td[(becomesmostimportant 81

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whenpredictingMCL,itseems)]TJ /F1 11.955 Tf 6.78 0 Td[('seffectsincreasewithincreasingprojectionintothefuture.FortheESTModel,thereisagreaterdiffernceinthemostsensitiveparametersdependingonwhatoutputisbeinginvestigated.ForCOE,lnandsourcelengtharemostimportant.Fortimeto1g/day,lnandlnarethemostimportant,closelyfollowedbysourcelength.ForthetimetoMCL,lnandAfarethemostimportantwithlnalsoplayinganimporantrole.Dispersivitywasneveridentiedasaparametertheoutputsweresensitivetoforeithermodel.Futureresearchcouldinvestigatewhetherdispersivitycouldbehandledasaknownparameterratherthanattingparameterwithoutaffectingsignicanteffectsonthemodeloutputs.Theprotocolspresentedherehelpintroducesourcestrengthfunctionsasametricinsitemanagement.Asis,theprotocolscannotproduceresultswithenoughcertaintytodomorethanobtaingeneraltimeframeuntilasitewillreachauxorconcentrationbenchmark.Futureworkshouldattempttoquantifytheuncertaintyassociatedwiththebesttparametercombinations.Additionally,futureworkcouldbedonewithsyntheticdatatodeterminehowmanyoftheinvestigatedttingparametersmustbeknownandwithinwhatrangetheymustbeknownbeforethealgorithmhasahighlevelofcertainty.Additionally,investigationintotheroleheterogeneityintheoweldsatthesitesplaysinthesuccessofthealgorithmshouldbeinvestigated.Iftheuncertaintyofthebesttparametersvaluescanbereducedandtheremaininguncertaintycanbequantied,theseprotocolscouldbecomereliableenoughtobeusedinmakingremedialdecisions. 82

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APPENDIXAHILLAFBDATA TableA-1. HillAFBPumpingData DateTCEConc.VolumePumpedCumulativeVolumePumpedg/Lm3m3 1/1/991110574734732/1/9993010495223/1/991048054529744/1/997807326112355/1/9918539339216276/1/9917838025518827/1/9946590601248358/1/9919105045129349/1/9999850448338210/1/9957250852423411/1/992368041442567612/1/9923680415258281/1/0028329068565132/1/00185398.5152480373/1/00875072393104304/1/00189885280107105/1/00237397138108486/1/00143552479113277/1/00180933166114938/1/0014059055115489/1/001588032991184710/1/00383600881193511/1/00156690691200412/1/00185865131121351/1/01250165326124612/1/01398315488129493/1/01311837186131354/1/0141753352131875/1/01570470210133979/1/012118438091473310/1/01194296.515711630411/1/0117675011131741712/1/01102675613180301/1/0290333479185092/1/0298200180186893/1/0210600027618965 83

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Table A-1 .Continued DateTCEConc.VolumePumpedCumulativeVolumePumpedg/Lm3m3 4/1/02118600155191205/1/02114750191193116/1/022001251497208087/1/022855001234220428/1/0296125615226579/1/02710305092316610/1/02879502542342011/1/021450001922361212/1/02204950271238831/1/0390950305241882/1/0397000181243693/1/03156500115244844/1/0319566795245795/1/03186000108246876/1/03190000180248677/1/03170500249251168/1/03181000160252769/1/032635001462542210/1/03353667682549011/1/03439100472553712/1/0355740052255891/1/0471900076256652/1/0466850076257413/1/0447375088258294/1/04279000272261015/1/04304150202263036/1/04247000222265257/1/04296000185267108/1/04351000145268559/1/043750001182697310/1/04410500862705911/1/042780001302718912/1/04335500140273291/1/05287500149274782/1/05493500191276693/1/0527300088277574/1/05210000379281365/1/05148000391285276/1/05123900374289017/1/058450027929180 84

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Table A-1 .Continued DateTCEConc.VolumePumpedCumulativeVolumePumpedg/Lm3m3 8/1/05710001275304559/1/05617503753083010/1/05708502623109211/1/05769332113130312/1/05104600160314631/1/0685450146316092/1/06102100214318233/1/06113300229320524/1/0634300455325075/1/0678400776332836/1/0691500484337677/1/0678800360341278/1/0674500323344509/1/06249002123466210/1/06373002423490411/1/06776002763518012/1/0694500191353711/1/0715700207355782/1/07118000210357883/1/07197000167359554/1/07165000127360825/1/074150093361756/1/0761264362397/1/07262000103624910/1/072730423629111/1/071570193631012/1/0718700363101/1/085880363102/1/0814300048363583/1/08226058364164/1/083430141365575/1/08351049366066/1/0870959366657/1/08391082367478/1/08279052367999/1/083200473684610/1/0816308863773211/1/08556009663869812/1/08223000181388791/1/0919400012139000 85

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APPENDIXBCOMPUTERCODES 1programplpump usereaddata 3 implicitnone 5 integer::i,j,k,l,m,n,o,p,q,ii,jj,mm 7doubleprecision::xr(119),tr(119),calcmd(119) doubleprecision::md data(119,3) 9doubleprecision::c0,m0,g,check,ceff,sqdiff,avgdiff,sum,ls,q0, avesum,mleft 11 q=119!numberoflinesindatafile 13ceff=)]TJ /F18 9.963 Tf 7.41 0 Td[(1e38 ls=)]TJ /F18 9.963 Tf 8.13 0 Td[(1.0d0 15 callgetdata(md data) 17 19sum=0.0d0 loopsum:doj=1,q 21sum=sum+md data(j,2) enddoloopsum 23 loopco:dok=250,350 25c0=k0.001d0 27loopmo:dol=8000,9000,10 m0=l1.0d0 29 loopg:doo=0,200 86

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31g=o0.10d0 33loopt:dop=1,q mleft=((((g)]TJ /F18 9.963 Tf 8.08 0 Td[(1)md data(p,3)c0)/(m0g))+(m0(1)]TJ /F18 9.963 Tf 8.44 0 Td[(g)))(1/(1)]TJ /F18 9.963 Tf 8.93 0 Td[(g)) 35if(isnan(mleft))then mleft=0.0d0 37endif if(mleft<=0.0d0)then 39calcmd(p)=0.0d0 else 41if(g/=1.d+00)then if(g/=0.5d+00)then 43if(ls>0.d+00)then calcmd(p)=((c0/m0g)((()]TJ /F18 9.963 Tf 8.6 0 Td[(md data(p,3)c0)/(ls(m0 g)))& 45+((m0(1)]TJ /F18 9.963 Tf 13.36 0 Td[(g))+((md data(p,3)c0)/(ls(m0g))))& dexp((g)]TJ /F18 9.963 Tf 14.17 0 Td[(1)ls(md data(p,1)365.250d0)))(g/(1 )]TJ /F18 9.963 Tf 13.36 0 Td[(g))) 47else calcmd(p)=(((c0/m0g)((((g)]TJ /F18 9.963 Tf 14.17 0 Td[(1)md data(p,3)c0) /(m0g))& 49+m0(1)]TJ /F18 9.963 Tf 13.35 0 Td[(g))(g/(1)]TJ /F18 9.963 Tf 13.35 0 Td[(g))))1000000 endif 51else calcmd(p)=(c0)]TJ /F18 9.963 Tf 14.47 0 Td[(((md data(p,3)c02)/(2m0))) 53endif else 55calcmd(p)=(c0dexp(()]TJ /F18 9.963 Tf 8.6 0 Td[(md data(p,3)c0)/m0)) endif 57endif if(isnan(calcmd(p)))then 59calcmd(p)=0.0d0 endif 87

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61enddoloopt 63avgdiff=0.0d0 sqdiff=0.0d0 65loopceff:doii=1,q avgdiff=avgdiff+((sum/q))]TJ /F18 9.963 Tf 14.47 0 Td[((md data(ii,2)))2 67sqdiff=sqdiff+(calcmd(ii))]TJ /F18 9.963 Tf 14.47 0 Td[((md data(ii,2)))2 enddoloopceff 69check=1)]TJ /F18 9.963 Tf 14.46 0 Td[((sqdiff/avgdiff) if(check>ceff)then 71ceff=check write(,'(12f15.5)'),c0,m0,g,ceff 73endif enddoloopg 75enddoloopmo enddoloopco 77 endprogram programestpump 2usereaddata usemaths 4 implicitnone 6 integer::i,j,k,l,m,n,o,p,q,ii,jj,mm 8doubleprecision::xr(119),tr(119),calcmd(119) doubleprecision::md data(119,3) 10doubleprecision::csol,fc,mu,sigma,check,ceff,sqdiff,avgdiff,sl,pv, h 12 q=119!numberoflinesindatafile 88

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14ceff=1e38 csol=1.10d0 16 callgetdata(md data) 18 loopmu:dok=0,10 20mu=k0.010d0 22loopsigma:dol=0,100 sigma=l0.010d0 24 loopfc:doo=0,10 26fc=o0.010d0 28loopsl:doi=0,10 sl=0.010d0i 30 looph:dojj=0,10 32h=jj0.01d0 34loopt:dop=1,q pv=((md data(p,3)(1/(3.14slsl))(1/h))) 36calcmd(p)=1000000fccsol(1.0d+00)]TJ /F18 9.963 Tf 14.48 0 Td[((0.5d+00+0.5d+00& dferf((dlog(pv))]TJ /F18 9.963 Tf 12.5 0 Td[(mu)/(sigmadsqrt(2.0d+00))))) 38if(isnan(calcmd(p)))then calcmd(p)=0.0d0 40endif enddoloopt 42 avgdiff=0.0d0 44sqdiff=0.0d0 loopceff:doii=1,q 46avgdiff=avgdiff+((sum/q))]TJ /F18 9.963 Tf 14.47 0 Td[((md data(ii,2)))2 89

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sqdiff=sqdiff+(calcmd(ii))]TJ /F18 9.963 Tf 14.47 0 Td[((md data(ii,2)))2 48enddoloopceff check=1)]TJ /F18 9.963 Tf 14.46 0 Td[((sqdiff/avgdiff) 50if(check>ceff)then ceff=check 52write(,'(12f15.8)'),mu,sigma,fc,sl,h,ceff endif 54enddolooph enddoloopsl 56enddoloopfc enddoloopsigma 58enddoloopmu 60endprogram programpltransect 2usegamdom usewdata 4useieee arithmetic 6implicitnone 8integer::i,j,k,l,m,n,o,p,q,ii,jj,mm,oo,a doubleprecision::xr(3),tr(3),calcmd(3) 10doubleprecision::md data(3,3) doubleprecision::vi,xoi,coi,moi,toi,axi,gi,check,ceff,sqdiff, avgdiff,sum,swi,shi 12 q=3!numberoflinesindatafile 14swi=1.0d0 shi=1.0d0 16ceff=)]TJ /F18 9.963 Tf 7.41 0 Td[(1e38 90

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18callreaddata(md data) 20sum=0.0d0 loopsum:doo=1,q 22sum=sum+md data(o,1) enddoloopsum 24 loopv:doa=6,14,2 26vi=0.01d0a 28loopx:doj=)]TJ /F18 9.963 Tf 8.07 0 Td[(4,4,2 xoi=j1.0d0 30dojj=1,q xr(jj)=md data(jj,2)+xoi 32enddo 34loopco:dok=6,14,2 coi=k1.10d00.1d0 36 loopmo:dol=300,700,100 38moi=l1.0d0 40loopto:dom=1966,1974,2 toi=m1.0d0 42domm=1,q tr(mm)=(md data(mm,3))]TJ /F18 9.963 Tf 9.01 0 Td[(toi)365.25d0 44enddo 46loopax:don=1,21,4 axi=n1.0d0 48 loopg:dooo=0,20 50gi=oo0.1d0 91

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52loopcalc:dop=1,q calcmd(p)=vic(gi,1.0d0,axi,1.0d0,1.0d0,tr(p),xr(p),0.0d0,0.0d0,moi ,1.0d0,1.0d0,0.0d0,vi,coi,0.0000000001d0,)]TJ /F18 9.963 Tf 8.13 0 Td[(1.0d0) 54if(ieee is nan(calcmd(p)))then calcmd(p)=0.0d0 56endif enddoloopcalc 58 avgdiff=0.0d0 60sqdiff=0.0d0 62loopceff:doii=1,q avgdiff=avgdiff+((sum/q))]TJ /F18 9.963 Tf 14.47 0 Td[((md data(ii,1)))2 64sqdiff=sqdiff+(calcmd(ii))]TJ /F18 9.963 Tf 14.47 0 Td[((md data(ii,1)))2 enddoloopceff 66ceff=1)]TJ /F18 9.963 Tf 14.86 0 Td[(sqdiff/avgdiff write(,'(8f15.5)'),vi,xoi,coi,moi,toi,axi,gi,ceff 68enddoloopg enddoloopax 70enddoloopto enddoloopmo 72enddoloopco enddoloopx 74enddoloopv 76endprogram programesttransect 2usestdom usewdata 4useieee arithmetic 92

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6implicitnone 8integer::i,j,k,l,m,n,o,p,q,ii,jj,mm,oo,a,kk,nn doubleprecision::xr(20),tr(20),calcmd(20) 10doubleprecision::md data(20,3) doubleprecision::vi,xoi,moi,toi,axi,gi,check,ceff,sqdiff,avgdiff, sum,swi,shi,sli,fci,sig,mu 12 q=20!numberoflinesindatafile 14swi=1.0d0 shi=1.0d0 16ceff=)]TJ /F18 9.963 Tf 7.41 0 Td[(1e38 18callreaddata(md data) 20sum=0.0d0 loopsum:doo=1,q 22sum=sum+md data(o,1) enddoloopsum 24 loopv:doa=10,12 26vi=0.01d0a 28loopx:doj=)]TJ /F18 9.963 Tf 8.07 0 Td[(2,2 xoi=j1.0d0 30dojj=1,q xr(jj)=md data(jj,2)+xoi 32enddo 34loopfc:dok=8,12 fci=k0.1d0 36 loopto:dom=1968,1972 93

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38toi=m1.0d0 domm=1,q 40tr(mm)=(md data(mm,3))]TJ /F18 9.963 Tf 9.01 0 Td[(toi)365.25d0 enddo 42 loopax:don=1,13,4 44axi=n1.0d0 46loopsl:dokk=1,5 sli=kk1.0d0 48 loopmu:donn=38,48 50mu=nn0.10d0 52loopsig:dooo=0,20 sig=oo0.1d0 54 loopcalc:dop=1,q 56calcmd(p)=vic(sig,mu,fci,1.0d0,axi,0.0d0,0.0d0,tr(p),xr(p),0.0 d0,0.0d0,1.0d0,1.0d0,sli,vi,0.0000001d0,)]TJ /F18 9.963 Tf 8.13 0 Td[(1.0d0) if(ieee is nan(calcmd(p)))then 58calcmd(p)=0.0d0 endif 60enddoloopcalc 62avgdiff=0.0d0 sqdiff=0.0d0 64 loopceff:doii=1,q 66avgdiff=avgdiff+((sum/q))]TJ /F18 9.963 Tf 14.47 0 Td[((md data(ii,1)))2 sqdiff=sqdiff+(calcmd(ii))]TJ /F18 9.963 Tf 14.47 0 Td[((md data(ii,1)))2 68enddoloopceff ceff=1)]TJ /F18 9.963 Tf 14.86 0 Td[(sqdiff/avgdiff 94

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70write(,'(9f15.5)'),sli,vi,xoi,fci,toi,axi,mu,sig,ceff enddoloopsig 72enddoloopmu enddoloopsl 74enddoloopax enddoloopto 76enddoloopfc enddoloopx 78enddoloopv 80endprogram programplotestintime 2usegamdom 4implicitnone 6doubleprecision::vi,xoi,coi,moi,toi,axi,gi,swi,shi,calcmd,p 8swi=1.0d0 shi=1.0d0 10vi=46.20d0 xoi=39.5290d0 12coi=79608.0480d0 moi=635976.50d0 14toi=5.8820d0 axi=70.6410d0 16gi=1.745410d0 18p=1970)]TJ /F18 9.963 Tf 9.6 0 Td[(toi dowhile(p<=2011) 20calcmd=(1000.0d0/365.25d0)vic(gi,1.0d0,axi,1.0d0,1.0d0,(p)]TJ /F18 9.963 Tf 7.84 0 Td[((1970)]TJ /F18 9.963 Tf 9.7 0 Td[(toi) ),60.0d0+xoi,& 95

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&0.0d0,0.0d0,moi,1.0d0,1.0d0,0.0d0,vi,coi,0.0000000001d0,)]TJ /F18 9.963 Tf 8.14 0 Td[(1.0d0) 22!if(ieee is nan(calcmd))then if(isnan(calcmd))then 24calcmd=0.0d0 endif 26print,p,calcmd p=p+1.0 28enddo 30endprogram programpltomcl 2 implicitnone 4 doubleprecision::v,xo,co,mo,to,ax,g,p,sw,sh,cs,ls 6 8cs=1000 sw=1.0d0 10sh=1.0d0 v=47.20d0 12co=79608.0480d0 mo=635976.50d0 14to=5.8820d0 g=1.745410d0 16ls=)]TJ /F18 9.963 Tf 8.13 0 Td[(1.0d0 18p=1971.0d0)]TJ /F21 9.963 Tf 7.71 0 Td[(to dowhile(cs>=0.001) 20if(g/=1.d+00)then if(g/=0.5d+00)then 22if(ls>=0.d+00)then 96

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cs=((co/mog)((()]TJ /F18 9.963 Tf 8.47 0 Td[(vswshco)/(ls(mog)))& 24+((mo(1)]TJ /F18 9.963 Tf 13.36 0 Td[(g))+((vswshco)/(ls(mog))))& dexp((g)]TJ /F18 9.963 Tf 14.17 0 Td[(1)ls(p)]TJ /F18 9.963 Tf 8.45 0 Td[((1970.0d0)]TJ /F21 9.963 Tf 7.72 0 Td[(to))))(g/(1)]TJ /F18 9.963 Tf 13.36 0 Td[(g))) 26else cs=((co/mog)((p)]TJ /F18 9.963 Tf 8.44 0 Td[((1970.0d0)]TJ /F21 9.963 Tf 7.71 0 Td[(to))(((g)]TJ /F18 9.963 Tf 14.17 0 Td[(1)vsw shco)/(mog))& 28+mo(1)]TJ /F18 9.963 Tf 13.35 0 Td[(g))(g/(1)]TJ /F18 9.963 Tf 13.35 0 Td[(g))) endif 30else cs=(co)]TJ /F18 9.963 Tf 14.47 0 Td[(((v(swsh)co2)/(2mo))(p)]TJ /F18 9.963 Tf 8.45 0 Td[((1970.0d0)]TJ ET 1 G 1 g q 2.989 w -1.49 -217.64 m -1.49 -197.86 l S Q 0 G 0 g 1 G 1 g q .398 w -3.19 -217.64 m -3.19 -197.86 l S Q 0 G 0 g q .398 w -3.19 -217.64 m -3.19 -197.86 l S Q 1 G 1 g q 0 -217.64 468 19.79 re f Q 0 G 0 g 1 G 1 g q 2.989 w 469.49 -217.64 m 469.49 -197.86 l S Q 0 G 0 g 1 G 1 g q .398 w 471.19 -217.64 m 471.19 -197.86 l S Q 0 G 0 g q .398 w 471.19 -217.64 m 471.19 -197.86 l S Q BT /F21 9.963 Tf 92.51 -211.71 Td[(to))) 32endif else 34cs=(codexp((p)]TJ /F18 9.963 Tf 8.45 0 Td[((1970.0d0)]TJ /F21 9.963 Tf 7.72 0 Td[(to))()]TJ /F18 9.963 Tf 8.47 0 Td[(v(swsh)co)/mo)) endif 36if(isnan(cs))then cs=0.0d0 38endif print,p,cs 40p=p+1.0 enddo 42 endprogram 1programplotestinspace usestdom 3 implicitnone 5 doubleprecision::vi,xoi,coi,toi,axi,mu,sigma,fc,csol,sli,calcmd, p 7 vi=46.20d0 97

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9xoi=39.5290d0 fc=79608.0480d0 11toi=5.8820d0 axi=70.6410d0 13mu=1.745410d0 csol=35999.0d0 15sigma=0.8790d0 sli=33.0d0 17 p=0 19dowhile(p<=8001) calcmd(p)=vic(gi,1.0d0,axi,1.0d0,1.0d0,toi+32.830d0,p,0.0d0,0.0d0, moi,1.0d0,1.0d0,0.0d0,vi,coi,0.0000000001d0,)]TJ /F18 9.963 Tf 8.14 0 Td[(1.0d0)(1000.0 d0/365.250d0) 21if(isnan(calcmd(p)))then calcmd=0.0d0 23endif write(,'(2f15.5)'),p,calcmd 25p=p+1.0 enddoloopcalc 27 endprogram programesttomcl 2usestdom 4implicitnone 6doubleprecision::vi,coi,toi,mu,sigma,fc,csol,sli,cs,p 8vi=46.20d0 fc=79608.0480d0 10toi=5.8820d0 98

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mu=1.745410d0 12csol=1.1 sigma=0.8790d0 14sli=0.070d0 16p=1971)]TJ /F18 9.963 Tf 9.6 0 Td[(toi dowhile(calcmd<=0.0001) 18pv=(p)]TJ /F18 9.963 Tf 7.85 0 Td[((1970)]TJ /F18 9.963 Tf 9.7 0 Td[(toi))v/sl cs=(fccsol(1.0)]TJ /F18 9.963 Tf 14.48 0 Td[((0.5+0.5& 20ferf((log(pv))]TJ /F18 9.963 Tf 12.51 0 Td[(mu)/(sigmasqrt(2.0))))))vi(1000.0d0/365.250 d0) if(isnan(cs))then 22calcmd=0.0d0 endif 24write(,'(2f15.5)'),p,cs p=p+1.0 26enddoloopcalc 28endprogram moduledomenico 2usemaths implicitnone 4 doubleprecision::t,x,y,z,ax,ay,az,sw,sh,sl,v,lp,r 6 !$ompthreadprivate(t,x,y,z,ax,ay,az,sw,sh,sl,v,lp,r) 8 contains 10 subroutineinit(tin,xin,yin,zin,axin,ayin,azin,& 12swin,shin,slin,vin,lpin,rin) 99

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14doubleprecision,intent(in)::axin,ayin,azin doubleprecision,intent(in)::tin 16doubleprecision,intent(in)::xin,yin,zin doubleprecision,intent(in)::vin 18doubleprecision,intent(in)::swin,shin,slin doubleprecision,intent(in)::lpin,rin 20 r=rin 22t=tin x=xin 24y=yin z=zin 26ax=axin ay=ayin 28az=azin sw=swin 30sh=shin sl=slin 32v=vin lp=lpin 34 endsubroutineinit 36 38functionfy() doubleprecision::fy 40fy=1.0d0 return 42endfunctionfy 44 functionfz() 46doubleprecision::fz 100

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fz=1.0d0 48return endfunctionfz 50 52functionb(tr) doubleprecision::b 54doubleprecision::tr doubleprecision::u,m,p,q,n,h,d 56doubleprecision::tmps(12) integer::i 58 if(lp>0.d+00)then 60!lambda p>0,degradationinplume u=vdsqrt(1+(4lpax)/v) 62 !print,f,r,x,u,tr,pi,sw,sh,v,lp,g 64tmps(1)=v/(v+u) tmps(2)=(rx+utr)/(2.d+00trdsqrt(piaxvr tr)) 66tmps(3)=dexp(((v)]TJ /F18 9.963 Tf 13.36 0 Td[(u)/(2.d+00axv)))]TJ /F18 9.963 Tf 15.13 0 Td[((((rx)]TJ /F18 9.963 Tf 13.35 0 Td[(utr)2) /(4.d+00axvrtr))) tmps(4)=v/(v)]TJ /F18 9.963 Tf 13.36 0 Td[(u) 68tmps(5)=(rx)]TJ /F18 9.963 Tf 13.36 0 Td[(utr)/(2.d+00trdsqrt(piaxvr tr)) tmps(6)=dexp(((v+u)/(2.d+00axv)))]TJ /F18 9.963 Tf 15.13 0 Td[((((rx+utr)2) /(4.d+00axvrtr))) 70tmps(7)=v/(2.d+00lpax) tmps(8)=(rx)]TJ /F18 9.963 Tf 13.63 0 Td[(vtr)/(2.d+00trdsqrt(piaxvr tr)) 72tmps(9)=dexp((x/ax))]TJ /F18 9.963 Tf 14.91 0 Td[(((lptr)/r))]TJ /F18 9.963 Tf 15.13 0 Td[((((rx+vtr)2.d +00)/(4axvrtr))) tmps(10)=v/(2.d+00rax) 101

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74tmps(11)=dexp((x/ax))]TJ /F18 9.963 Tf 14.91 0 Td[(((lptr)/r)) tmps(12)=dferfc((rx+vtr)/(2.d+00dsqrt(axvrtr ))) 76 b=(tmps(1)tmps(2)tmps(3))+(tmps(4)tmps(5)tmps(6))+& 78(tmps(7)tmps(8)tmps(9)))]TJ /F18 9.963 Tf 14.47 0 Td[((tmps(10)tmps(11)tmps(12)) 80return else 82!lambda p=0,nodegradationinplume(typicallycoupledwith lambda s=0) d=axv 84b=(1/dsqrt(pi))& (& 86dexp()]TJ /F18 9.963 Tf 7.97 0 Td[(((rx)]TJ /F18 9.963 Tf 13.63 0 Td[(vtr)2)/(4drtr))& (& 88(& (v/(2dsqrt(drtr)))+& 90(dr(rx)]TJ /F18 9.963 Tf 13.64 0 Td[(vtr))/(4(drtr)1.5)& )& 92+(& dsqrt((tr(v2))/(dr))& 94(& (rx)]TJ /F18 9.963 Tf 13.63 0 Td[(vtr)2/(4drtr2)+& 96(v(rx)]TJ /F18 9.963 Tf 13.64 0 Td[(vtr)/(2drtr))& )& 98+(v2/(2drdsqrt((v2tr)/(dr))))& )& 100)& +(v/(2dsqrt(drtr))& 102)]TJ /F18 9.963 Tf 14.46 0 Td[((dr(rx+vtr))/(4(drtr)1.5))& dexp((vx/d))]TJ /F18 9.963 Tf 14.47 0 Td[((rx+vtr)2/(4drtr))& 104(1+(vx/d)+(v2tr/(dr)))& 102

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)& 106)]TJ /F18 9.963 Tf 14.47 0 Td[((v2/(2dr))exp(vx/d)& dferfc((rx+vtr)/(2dsqrt(drtr))) 108return endif 110 return 112endfunction 114 endmoduledomenico 1modulessf gamma implicitnone 3 doubleprecision::g,c0,ls,sw,sh,v,m0 5 !$ompthreadprivate(g,c0,ls,sw,sh,v,m0) 7 contains 9subroutineinit(gin,c0in,m0in,swin,shin,vin,lsin) doubleprecision,intent(in)::gin 11doubleprecision,intent(in)::c0in doubleprecision,intent(in)::m0in 13doubleprecision,intent(in)::swin doubleprecision,intent(in)::shin 15doubleprecision,intent(in)::vin doubleprecision,intent(in)::lsin 17 g=gin 19c0=c0in ls=lsin 21sw=swin 103

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sh=shin 23v=vin m0=m0in 25endsubroutineinit 27 functioncs(tr) 29doubleprecision::cs doubleprecision::tr,td 31 if(g<0.d+00)then 33cs=c01.d+00 return 35endif 37if(g/=1.d+00)then if(g/=0.5d+00)then 39if(ls>0.d+00)then cs=(c0/m0g)((()]TJ /F18 9.963 Tf 8.47 0 Td[(vswshc0)/(ls(m0g)))& 41+((m0(1)]TJ /F18 9.963 Tf 13.36 0 Td[(g))+((vswshc0)/(ls(m0g))))& dexp((g)]TJ /F18 9.963 Tf 14.17 0 Td[(1)lstr))(g/(1)]TJ /F18 9.963 Tf 13.35 0 Td[(g)) 43else cs=(c0/m0g)(tr(((g)]TJ /F18 9.963 Tf 14.17 0 Td[(1)vswshc0)/( m0g))& 45+m0(1)]TJ /F18 9.963 Tf 13.35 0 Td[(g))(g/(1)]TJ /F18 9.963 Tf 13.35 0 Td[(g)) endif 47else cs=c0)]TJ /F18 9.963 Tf 14.47 0 Td[(((v(swsh)c02)/(2m0))tr 49endif else 51cs=c0dexp(tr()]TJ /F18 9.963 Tf 8.47 0 Td[(v(swsh)c0)/m0) endif 53 104

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return 55endfunctioncs 57 endmodulessf gamma modulegamdom 2usemaths usedquadpack 4usedomenico,dinit=>init,swd=>sw,shd=>sh,vd=>v usessf gamma,ginit=>init 6 implicitnone 8 contains 10subroutineinit(gin,rin,axin,ayin,azin,tin,xin,yin,zin,m0in,& swin,shin,slin,vin,c0in,lsin,lpin) 12doubleprecision,intent(in)::gin doubleprecision,intent(in)::axin 14doubleprecision,intent(in)::tin doubleprecision,intent(in)::xin,yin,zin 16doubleprecision,intent(in)::vin doubleprecision,intent(in)::swin,shin,slin 18doubleprecision,intent(in)::lpin doubleprecision,intent(in)::m0in 20doubleprecision,intent(in)::lsin doubleprecision,intent(in)::c0in 22doubleprecision,intent(in)::ayin,azin,rin 24calldinit(tin,xin,yin,zin,axin,ayin,azin,& swin,shin,slin,vin,lpin,rin) 26 callginit(gin,c0in,m0in,swin,shin,vin,lsin) 105

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28endsubroutineinit 30functionc(gin,rin,axin,ayin,azin,tin,xin,yin,zin,m0in,& swin,shin,slin,vin,c0in,lsin,lpin) 32doubleprecision::c doubleprecision,intent(in)::gin,rin 34doubleprecision,intent(in)::axin,ayin,azin doubleprecision,intent(in)::tin 36doubleprecision,intent(in)::xin,yin,zin doubleprecision,intent(in)::vin 38doubleprecision,intent(in)::swin,shin,slin doubleprecision,intent(in)::lpin 40doubleprecision,intent(in)::m0in doubleprecision,intent(in)::lsin 42doubleprecision,intent(in)::c0in 44doubleprecision::abserr doubleprecision::ci 46doubleprecision,parameter::epsabs=1.0d)]TJ /F18 9.963 Tf 7.52 0 Td[(12 doubleprecision,parameter::epsrel=1.0d)]TJ /F18 9.963 Tf 7.3 0 Td[(6 48doubleprecision,dimension(6003+1000)::work integer,dimension(1000)::iwork 50 integer,parameter::key=1 52integer::neval,ier 54callinit(gin,rin,axin,ayin,azin,tin,xin,yin,zin,m0in,& swin,shin,slin,vin,c0in,lsin,lpin) 56 !callforSLATECintegrater 58!calldqag(fcsb,0.d+00,t,epsabs,epsrel,key,ci,abserr,& !neval,ier,1000,10000,100,iwork,work) 60 106

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calldqag(f,0.d+00,t,epsabs,epsrel,key,ci,abserr,neval,ier) 62 c=dabs(ci) 64endfunctionc 66functionf(tr) doubleprecision::f 68doubleprecision::tr,td 70!sourcewilleventuallydeplete.. if(g<1.d+00)then 72!calculatetimetodepletion td=dlog((vdswshc0)/(lsm0+vdswshc0))& 74/((g)]TJ /F18 9.963 Tf 14.17 0 Td[(1)ls) 76if((t)]TJ /F18 9.963 Tf 15.1 0 Td[(tr)>td)then !savecpucyclesifsourcedepletedatrequestedtime 78f=0.d+00 return 80endif endif 82 f=cs(t)]TJ /F18 9.963 Tf 15.1 0 Td[(tr)b(tr) 84return endfunctionf 86 endmodulegamdom 1modulessf streamtube use::maths 3implicitnone 5doubleprecision::pv,v,sl 107

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doubleprecision::slnt,ulnt,fc 7doubleprecision,parameter::csol=1.1d+00!Solubilitylimit,g/L 9!$ompthreadprivate(pv,v,sl,slnt,ulnt,fc) 11contains subroutineinit(slntin,ulntin,fcin,slin,vin) 13doubleprecision,intent(in)::slin doubleprecision,intent(in)::slntin,ulntin,fcin 15doubleprecision,intent(in)::vin 17slnt=slntin ulnt=ulntin 19sl=slin v=vin 21fc=fcin endsubroutineinit 23 functioncs(tr) 25doubleprecision::cs doubleprecision::tr 27 pv=trv/sl 29cs=fccsol(1.0d+00)]TJ /F18 9.963 Tf 14.49 0 Td[((0.5d+00+0.5d+00& dferf((dlog(pv))]TJ /F18 9.963 Tf 14.7 0 Td[(ulnt)/(slntdsqrt(2.0d+00))))) 31 return 33endfunctioncs endmodulessf streamtube modulestdom 2usemaths usedquadpack 108

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4usedomenico,dinit=>init usessf streamtube,sinit=>init 6 implicitnone 8 contains 10subroutineinit(slntin,ulntin,fcin,rin,axin,ayin,azin,tin,xin,yin ,zin,& swin,shin,slin,vin,lsin,lpin) 12doubleprecision,intent(in)::slntin,ulntin,fcin doubleprecision,intent(in)::axin,ayin,azin 14doubleprecision,intent(in)::rin doubleprecision,intent(in)::tin 16doubleprecision,intent(in)::xin,yin,zin doubleprecision,intent(in)::vin 18doubleprecision,intent(in)::swin,shin,slin doubleprecision,intent(in)::lpin 20doubleprecision,intent(in)::lsin 22calldinit(tin,xin,yin,zin,axin,ayin,azin,& swin,shin,slin,vin,lpin,rin) 24 callsinit(slntin,ulntin,fcin,slin,vin) 26endsubroutineinit 28functionc(slntin,ulntin,fcin,rin,axin,ayin,azin,tin,xin,yin,zin ,& swin,shin,slin,vin,lsin,lpin) 30doubleprecision,intent(in)::slntin,ulntin,fcin doubleprecision,intent(in)::axin,ayin,azin,rin 32doubleprecision,intent(in)::tin doubleprecision,intent(in)::xin,yin,zin 34doubleprecision,intent(in)::vin 109

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doubleprecision,intent(in)::swin,shin,slin 36doubleprecision,intent(in)::lpin doubleprecision,intent(in)::lsin 38 doubleprecision::c 40doubleprecision::abserr doubleprecision::ci 42doubleprecision,parameter::epsabs=0.0d)]TJ /F18 9.963 Tf 7.52 0 Td[(12 doubleprecision,parameter::epsrel=1.0d)]TJ /F18 9.963 Tf 7.3 0 Td[(6 44 integer,parameter::key=6 46integer::neval,ier 48callinit(slntin,ulntin,fcin,rin,axin,ayin,azin,tin,xin,yin, zin,& swin,shin,slin,vin,lsin,lpin) 50 calldqag(f,0.0d+00,t,epsabs,epsrel,key,ci,abserr,neval,ier) 52 c=dabs(ci)fy()fz() 54endfunctionc 56functionf(tr) doubleprecision::f 58doubleprecision,intent(in)::tr f=cs(t)]TJ /F18 9.963 Tf 15.1 0 Td[(tr)b(tr) 60endfunctionf endmodulestdom 1modulereaddata implicitnone 3integer,parameter::num md=119 110

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5contains subroutinegetdata(md data) 7!character32,dimension(num md)::well names doubleprecision,dimension(num md,3)::md data 9 integer::i,ios 11character255::line 13i=1 open(unit=1,file='data/data.csv') 15do read(unit=1,fmt='(a)',iostat=ios)line 17if(ios/=0)then exit 19endif read(unit=line,fmt=)md data(i,1),md data(i,2),md data(i,3) 21i=i+1 enddo 23 close(1) 25return endsubroutine 27 endmodulereaddata modulemaths 2implicitnone 4doubleprecision,parameter::pi=3.14159265358979323846264338328d+00 6contains 8functiondferfc(zer) 111

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doubleprecision::dferfc 10doubleprecision,intent(in)::zer 12if(zer<0.d+00)then dferfc=2.d+00)]TJ /F18 9.963 Tf 14.43 0 Td[(derfc(dabs(zer)) 14else dferfc=derfc(zer) 16endif return 18endfunction 20functiondferf(zer) doubleprecision::dferf 22doubleprecision,intent(in)::zer 24if(zer<0.d+00)then dferf=)]TJ /F18 9.963 Tf 8.13 0 Td[(1.d+00derf(dabs(zer)) 26else dferf=derf(zer) 28endif return 30endfunction 32functiondsec(zer) doubleprecision::dsec 34doubleprecision,intent(in)::zer 36dsec=1.d+00/dcos(zerpi/180.d+00) return 38endfunction 40endmodulemaths 112

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REFERENCES Basu,N.,Fure,A.,Jawitz,J.,2008.Simpliedcontaminantsourcedepletionmodelsasanalogsofmultiphasesimulators.J.Contam.Hydrol.97,87. Basu,N.,Rao,P.,Poyer,I.,Nandy,S.,Mallavarapu,M.,Naidu,R.,Davis,G.,Patterson,B.,Annable,M.,Hateld,K.,2009.Integrationoftraditionalandinnnovativecharacterizationtechnniquesforux-basedassessmentofDenseNon-aqueousPhaseLiquid(DNAPL)sites.J.Contam.Hydrol.105,161. BEMSystems,Inc.,2002.HangarKSolidWasteManagementUnitC022CapeCanaveralAirForceStation,Florida:CorrectiveMeasuresStudyReport,PreparedforU.S.AirForceSpaceCommand. CH2MHill,2008.RemeidalActionatOperableUnit3AreasCandD,PreparedforNavalFacilitiesEngineeringCommand. Chen,X.,Jawitz,J.,2009.ConvergenceofDNAPLSourceSTrengthFunctionswithSiteAge.Environ.Sci.Technol.43,9374. COREEngineeringConstruction,Inc.,2009.HangarK-CMIPerformancyMonitoringPlan,PreparedforU.S.AirForceSpaceCommand. EPA,2011.ListofContaminantsandtheirMaximumContamninatLevel(MCLs). EuropeanUnion,2008.SimLab. Falta,R.,Basu,N.,Rao,R.,2005a.AssessingimpactsofpartialmassdepletioninDNAPLsourcezones:II.Couplingsourcestrengthfunctionstoplumeevolution.J.Contam.Hydrol.79,45. Falta,R.,Rao,R.,Basu,N.,2005b.AssessingtheimpactsofpartialmassdepletioninDANPLsourcezones:I.Analyticalmodelingofsourcestrengthfunctionsandplumeresopnse.J.Contam.Hydrol.78,259. Falta,R.,Stacy,M.,Ahsanuzzaman,A.,Wang,M.,Earle,R.,2007.REMChlorRemediationEvaluationModelforChlorinatedSolventsUser'sManualVersion1.0.Comput.App.Eng.Educ. Fure,A.,Jawitz,J.,Annable,M.,2006.DNAPLsourcedepletion:Linkingarchitectureanduxresponse.J.Contam.Hydrol.85,118. Guyonnet,D.,Neville,C.,2004.Dimensionlessanalysisoftwoanalyticalsolutionsfor3-dsolutetransportingroundwater.J.Contam.Hydrol.75,141. Harbaugh,A.,2005.MODFLOW-2005,TheU.S.GeologicalSurveyModularGround-WaterModel-theGround-WaterFlowProcess. HardingLawsonAssociates,2008.RemedialInvestigationandFeasibilityStudyOperableUnit3,PreparedforNavalFacilitiesEngineeringCommand. 113

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Javandel,I.,Doughtry,C.,Tsang,C.,1984.GroundwaterTransport:HandbookofMathematicalModels.WaterResourcesMonograph.Am.Geophys.Union,Washington,DC. Jawitz,J.,Annable,M.,Demmy,G.,Rao,P.,2003.Estimatingnonaqueousphaseliquidspatialvariabilityusingpartitioningtracerhighertemporalmoments.WaterResourc.Res.39,1192. Jawitz,J.,Fure,A.,Demmy,G.,Berglund,S.,Rao,P.,2005.Groundwatercontaminantuxreductionresultingfromnonaqueousphaseliquidmassreduction.WaterResourc.Res.41. Kubert,M.,Finkel,M.,2006.Contaminantmassdischargeestimationingroundwaterbasedonmulti-levelpointmeasurements:Anumericalevaluationofexpecterrors.J.Contam.Hydrol.84,55. Li,S.,Liu,Q.,2004.InteractiveGroundwater(IGW):AnInnovativeDigitalLaboratoryforGroundwaterEducationandResearch.Comput.App.Eng.Educ.11. McCarty,P.,2010.Groundwatercontaminationbychlorinatedsolvents:History,remediationtechnologiesandstrategies.In:Stroo,H.,Ward,C.(Eds.),InSituRemediationofChlorinatedSolventPlumes.SERDP/ESTCPEnvironmentalRemediationTechnology.SpringerNewYork,pp.1. Morris,M.,1991.Factorialsamplingplansforpreliminarycomputationalexperiments.Tehnometrics33,161. Nash,J.,Sutcliffe,J.,1970.Riverowforecastingthroughconceptualmodeslpart1-Adiscussionofprinciples.J.Hydrol.10,282. Parker,J.,Kim,U.,Widdowson,M.,Kitanidis,P.,Gentry,R.,2010.Effectsofmodelformulationandcalibrationdataonunceratintyindensenonaqueousphaseliquidssurcedissoluitonpredictions.WaterResourc.Res.46,12517. Parker,J.,Park,E.,2004.Modelingeld-scaledensenonaqueousphaseiquiddissolutionkineticsinheterogenousaquifers.WaterResourc.Res.40,5109. Patterson,B.,Megharaj,M.,Barski,M.,Ying,G.,Briegel,D.,Davis,G.,Chen,Z.,Fisher,S.,Kookana,R.,2011.Massdepletion-massuxredutionrelationsyhipsduringpumpingusedtodeterminesourcezonemassofareactivebrominated-solventDNAPL.In:GQ10:GroundwaterQualityManagementinaRapidlyChangingWorld(Proc.7thInternationalGroundwaterQualityConferenceheldinZurich,Switzerland,13-18June2010).IAHSPubl342.pp.136. Piessens,R.,deDoncker-Kapenger,E.,Ueberhuber,C.,Kahaner,D.,1983.QUADPACK:ASubroutinPakcageofAutomaticIntegration.SpringerVerlag. 114

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Rao,P.,Jawitz,J.,Eneld,C.,Falta,R.,Annable,M.,Wood,A.,2001.Technologyintegrationforcontaminatedsiteremediation:cleanupgoalsandperformancemetrics.GroundWaterQuality,410. TetraTech,2008.MonitoringEvent10May2008ResutlsReportforSite07:CalfPasturePoint,PreparedforNavalFacilitiesEngineeringCommanMid-Atlantic. URS,2005.FlowandContaminantTransportModelReportOperableUnit2,PreparedforAirForceCenterforEnvironemtnalExcellence. Zheng,C.,Wang,P.,1999.MT3DMS:AModularThree-DimensionalMultispeciesTransportModelforSimulationofAdvection,Dispersion,andChemcialReactionsofContaminantsinGroundwaterSystems;DocumentationandUser'sGuide. 115

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BIOGRAPHICALSKETCH RachelwasborntoJosephandEllenDonahuein1986inWiesbaden,Germany.AftermovingtheUnitedStates,shelivedwithherparents,brother,andsisterinIllinois,Oklahoma,Tennessee,andPennsylvania.HerfamilymovedtoSt.Augustine,FloridarightbeforehersenioryearofhighschoolwhereRachelgraduatedfromBartramTrailHighSchoolin2005.Directlyfollowingherhighschoolgraduation,RachelenteredintotheUniversityofFloridawhereshereceivedherBachelorofScienceinEnvironmentalEngineeringwithhonorsin2009.Whilecompletingherundergraduatestudies,RachelparticipatedinUF'sEngineersWithoutBordersCambodiaproject,internedatDr.Townsend'sconsultingrm,InnovativeWasteConsultingServices,andworkedasaresearchassistantforDrs.MazyckandAnnable.Afterreceivingherbachelor's,RachelcontinuedherworkwithDr.AnnablewhilepursuingherMasterofEngineeringinEnvironmentalEngineeringandcompletingthehydrologicsciencesacademiccluster.Afterreceivinghermaster's,shewillentertheenvironmentalconsultingindustrywithGeosyntecConsultants. 116